EXCHANGE 


THE   PROBLEM  OF  SPACE 

IN  JEWISH  MEDIAEVAL 

PHILOSOPHY 


COLUMBIA  UNIVERSITY  PRESS 
SALES  AGENTS 

New  York: 
LEMCKE  &  BUECHNER 
30-32  West  27TH  Street 

London : 

HUMPHREY  MILFORD 

Amen  Corner,  E.C. 


COLUMBIA  UNIVERSITY  ORIENTAL  STUDIES 
Vol.  XI 


THE  PROBLEM  OF  SPACE  IN 

JEWISH 
MEDIAEVAL  PHILOSOPHY 


ISRAEL  ISAAC  EFROS 


Submitted  in  Partial  Fulfilment  of  the  Requirements 

for  the  Degree  of  Doctor  of  Philosophy,  in  the 

Faculty  of  Philosophy,  Columbia  University 


COLUMBIA  UNIVERSITY  PRESS 
1917 


PRINTED   AT   OXFORD,    ENGLAND 

BY   FREDERICK   HALL 
PRINTER    TO    THE    UNIVERSITY 


NOTE 

In  the  ordinary  treatises  dealing  with  philosophical 
problems  the  effort  expended  towards  their  solution  by 
the  Jewish  philosophers  of  the  Middle  Ages  is  accorded 
a  very  small  space.  This  is  due  to  two  causes.  The 
writings  of  these  thinkers  are  not  always  and  readily 
accessible  in  translations,  and  those  scholars  who  are 
acquainted  with  their  writings  at  first  hand  have  failed  to 
put  forward  the  views  they  have  expressed  upon  these 
problems.  It  is,  therefore,  with  pleasure  that  I  present  the 
following  exposition  of  one  of  them — that  of  Space — as 
that  subject  was  discussed  in  Jewish  circles  during  the 
Middle  Ages ;  and  especially  as  Dr.  Efros  submits  their 
standpoint  as  a  possible  solution  of  the  vexed  question. 
RICHARD  GOTTHEIL. 
Nov.  15,  1 9 16. 


383545 


IN  MEMORY  OF  MY  DEAR  SISTER 

ROSE 

WHO  PASSED  AWAY  IN  THE  BLOOM  OF  LIFE 

THIS  IS  SORROWFULLY  DEDICATED 


CONTENTS 

PAGE 

Introduction i 

CHAPTER  I 

Empirical  Space ii 

I.  Space  and  Spirit 22 

II.  Space  and  Matter 32 

III.  Infinite  Divisibility 46 

CHAPTER  II 

Absolute  Space 61 

I.  Space  versus  Place 65 

II.  The  Void        ........  71 

CHAPTER  III 

Infinite  Space 88 

Conclusion no 

APPENDIX 

Glossary  of  some  Hebrew  Philosophical 
terms  in  connexion  with  the  subject  of 
Space       .       . "7 

INDEX 123 


THE  PROBLEM  OF  SPACE  IN  JEWISH 
MEDIAEVAL  PHILOSOPHY 

I  TRUST  that  the  term  '  Jewish  Philosophy '  does  not 
require  any  apology;  indeed,  I  should  owe  the  reader 
a  greater  apology  were  I  to  attempt  to  give  any.  The 
famous  or  infamous  indictment  of  Renan l  that  the  Jews 
are  destitute  of  any  philosophic  talent  is  best  refuted  by 
expository  works  which  bring  to  light  the  depths  of  Jewish 
thought.  The  refutation  was  begun  by  Solomon  Munk, 
and  is  still  continued  by  every  monograph  that  has  appeared 
on  the  subject.  As  far  as  the  problem  of  space  is  con- 
cerned, a  problem  that  has  baffled  human  thought  ever 
since  the  days  of  Zeno  of  Elea,  I  hope  that  the  subsequent 
pages  will  serve  as  a  testimony  of  Jewish  profoundness  of 
thought  and  Jewish  comprehensiveness  of  the  grave  antino- 
mies that  this  difficult  problem  presents. 

The  scope  of  this  work  is  limited,  as  the  title  indicates, 
to  Mediaeval  Jewish  Philosophy,  i.e.  to  that  epoch  in 
Jewish  thought  which  was  inaugurated  by  Isaac  Israeli  of 
Kairwan,  an  older  contemporary  of  Saadya,  and  culminated 
in  Don  Isaac  Abrabanel— a  period  of  five  centuries  least 
familiar  to  the  general  student  of  philosophy,  but  which 
produced  the  choicest  fruits  of  the  maturing  Jewish 
intellect.  I  am  aware  of  the  abundance  of  ideas  relative 
to  the  problem  of  space  which  are  harboured  in  the 
Talmudic  and  Midrashic  literature ;  but  their  influence  on 

1  See  his  Histoire  des  langnes  st'tnitiques,  I,  i. 


2  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

the  philosophy  of  the  period  under  discussion  is,  as  far  as 
our  problem  is  concerned,  of  no  great  importance,  and  is 
therefore  omitted.  For  a  similar  reason  I  shall  not  deal 
here  with  Philo's  views  on  space,2  or,  on  the  other  side, 
with  the  views  of  Spinoza  and  others,  especially  our  great 
contemporaries  Hermann  Cohen  and  Henri  Bergson. 
Nevertheless,  should  the  reader  resent  the  limitations  that 
the  term  '  Mediaeval '  imposes,  I  shall  attempt  some  day  to 
resume  the  discussion  and  deal  with  those  views  that  are 
here  out  of  place. 

Introduction 

I.  On  the  surface,  the  idea  of  space  is  comparatively 
simple  and  intelligible.  It  is  the  idea  of  extensity  of  things, 
the  idea  of  an  external  world  that  is  not  a  mere  pin-point, 
all  the  parts  of  which  being  coalesced  and  compressed  to 
form  a  non-magnitudinal  and  indivisible  unity,  but  stretched 
out  and  extended  around  us,  all  the  parts  of  which  are 
lying  side  by  side  of  one  another,  and  thus  capable  of  being 
measured.  We  perceive  this  extensity  of  things  and  the 
'  alongsidedness '  of  its  parts,  by  our  visual  and  tactual  and 
muscular  senses.  When  we  move  our  eye  to  circumspect 
a  landscape,  we  have  a  sense  of  its  range  or  extensiveness. 
When  we  lay  our  hand  over  this  desk,  we  have  a  sense  of 
a  greater  area  than  when  we  lay  our  hand  over  a  pin-point. 
And  when  we  furthermore  move  our  hand  so  as  to  describe 
a  circle,  we  feel  a  vastness  around  us.  And  now  when  we 
gather  our  perceptions  of  extended  objects,  and  employ 
the  method  of  generalization  and  abstraction,  we  arrive  at 

2  As  for  Philo's  views  on  space,  the  reader  may  find  something  in 
Leisegang's  Die  Raumtheorie  im  sp'dteren  Platonismus  (Weida  i.  Th. :  Thomas 
&  Hubert,  1911),  but  the  account  is  by  no  means  satisfactory. 


INTRODUCTION  3 

the  concept  of  cxtensity  occupied  or  not  occupied  by 
concrete  objects — the  concept  of  pure  space. 

Yet  when  we  come  to  analyse  this  common  conception 
of  space  we  find  ourselves  beset  with  puzzling  problems 
and  baffling  antinomies.  The  notion  of  space,  I  said,  lies 
in  the  alongsidedness  of  parts.  But  those  parts  themselves 
in  order  to  be  perceived  must  be  composed  of  smaller 
parts,  and  so  on  ;  since  the  perception  of  any  extended 
quantity  involves  a  perception  of  parts.  But  what  of  the 
tiniest  speck,  the  minimum  sensibile,  in  which  no  parts 
seem  to  be  present ;  how  is  it  possibly  perceived  ?  And  if 
that  is  true,  every  body  is  composed  of  an  infinite  number 
of  particles,  or,  in  other  words,  every  finite  object  around 
us,  from  the  mountain  height  to  the  grain  of  sand,  is  really 
infinite.  Thus  an  ant  moving  over  a  blade  of  grass  is 
moving  over  an  infinite,  and  when  you  have  moved  over 
from  one  corner  of  the  room  to  the  other,  you  have  com- 
pleted an  infinite  series  of  points.     All  of  which  is  absurd. 

Leaving  the  question'  whether  space  is  infinite  in 
division,  we  may  ask  whether  space  is  infinite  in  extent. 
We  conceive  a  thing  when  we  know  it  or  seem  to  know  it 
definitely,  while  infinity  carries  with  it  an  indefinite  and 
indeterminate  element,  which  admits  of  no  conception.  A 
definite  knowledge  of  a  thing  implies  the  ability  to  compare 
it  to  others  and  distinguish  it  from  others.  But  the  infinite 
is  incomparable  and  indistinguishable.  Yet,  on  the  other 
hand,  if  space  is  finite  and  bounded,  the  question  is :  By 
what  is  it  bounded  ?  What  is  beyond  its  boundary  ?  And 
what  if  a  thing  were  to  be  carried  beyond  the  realm  of 
space ;  would  it  shrink  into  nothingness  ? 

One  more  question:  Is  space  itself  material  or  im- 
material ?     It  could  not  be  material,  for  a  thing  could  not 

b  a 


4  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

occupy  another  unyielding  material  thing  without  violating 
the  law  of  impenetrability.  If  immaterial,  what  is  it  ? 
What  is  meant  by  an  immaterial  something  existing  in  the 
external  world?  Perhaps  it  is  not  an  external  reality. 
Perhaps  it  is  a  mere  mental  illusion,  one  of  those  illusions 
with  which  the  mind  is  wont  to  deceive  mankind.  But  is 
it  conceivable  that  the  objective  reality  is  unspatial,  that 
it  has  no  magnitude  whatsoever,  that  this  vast  universe 
with  its  stars  and  planets  is  really  a  mere  geometrical  point 
located  nowhere  except  in  the  mind  of  the  mathematician  ? 
If  space  is  an  illusion,  why  cannot  the  elephant  escape 
through  the  key-hole?  To  make  space  mental  does  not 
make  matters  more  conceivable. 

Such  are  the  difficulties  which  present  themselves  in 
connexion  with  the  notion  of  space.  The  deeper  the  mind 
delves  into  the  problem,  the  greater  the  tangle.  It  is  one 
of  the  sphinxes  in  the  deserts  of  thought.  From  the  dawn 
of  speculation  we  find  space  to  be  one  of  the  most  promi- 
nent objects  of  investigation  ;  Zeno,  Plato,  and  Aristotle 
bent  their  great  intellects  on  the  solution  of  space  ;  colossal 
systems  of  science  were  reared  on  the  notion  of  space.  Yet 
the  meaning  of  space  has  remained  a  mystery  till  the  present 
day.   Indeed,  the  difficulties  seem  to  increase  with  the  time. 

It  would  be  preposterous  of  course  to  claim  that  the 
Jews  were  cognizant  of  all  these  difficulties  that  the  modern 
era  has  introduced.  If  we  turn  to  examine  the  views  on 
space  maintained  by  the  two  greatest  of  Greek  thinkers, 
who  had  such  an  enormous  influence  on  Jewish  thought, 
we  will  get  a  notion  of  the  type  of  problems  that  we  will 
have  to  deal  with  in  the  following  chapters.  In  addition, 
it  will  present  us  the  sources  and  the  starting-point  for  the 
views  that  are  to  be  discussed  in  this  study. 


introduction  5 

Plato's  Conception  of  Space 
II.  Students  of  Plato  are  not  in  agreement  as  to  his 
view  on  space.  Some  maintain  that  in  Plato's  conception 
space  is  the  primaeval  matter,  the  original  substrate  which 
was  fashioned  by  the  Demiurgus  into  all  perceptible  objects, 
that  it  is  the  raw  material  out  of  which  the  great  artisan 
created  all  things.  In  support  of  this  interpretation  they 
fall  back  upon  Aristotle,  who  in  his  Physics,  IV,  4  remarks 
as  follows:  'Hence  also  Plato  in  the  Timaeus  says  that 
matter  and  a  receptacle  are  the  same  thing.  For  that 
which  is  capable  of  receiving  and  a  receptacle  are  the  same 
thing.'  Thus  Aristotle  makes  Plato — and  who  would 
understand  Plato  better  than  his  illustrious  disciple? — 
identify  space  with  matter,  pre-existing  and  receiving  all 
created  things.  Hence  also  all  mediaeval  philosophers 
unanimously  assumed  that  Plato  affirmed  the  eternity  of 
matter.  On  the  other  hand,  there  are  many  scholars  who 
claim  that  Aristotle  misunderstood  Plato,  and  that  accord- 
ing to  the  latter  space  and  matter  are  not  identical,  but 
two  distinct  and  separate  beings.3 

Now,  in  favour  of  the  former  view,  the  following  argu- 
ments are  generally  adduced.  Plato  speaking  about  the 
third  yevos,  the  abiding  substrate  in  the  incessant  mutation 
of  phenomena,  compares  it  to  the  gold  that  is  moulded 
into  all  sorts  of  figures,  to  the  wax  that  is  impressed  by 
the  seal.4  The  elements,  fire,  air,  water,  earth,  are  not 
four  varieties  of  Being,  four  different  essences,  but  mere 
states  or  modes  of  one  sensuous  mass.  '  Fire  is  that  part 
of  her  nature  which  from  time  to  time  is  inflamed,  and 

3  For  a  detailed  bibliography  of  the  two  views,  see  Zeller's  Plato  and  the 
Older  Academy,  ch.VII,  notes  18,  20,  and  also  his  Platonische  Studien,  212,  222. 
*  Tim.,  p.  50. 


6  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

water  that  which  is  moistened,  and  that  the  molten  sub- 
stance becomes  earth  and  air  in  so  far  as  she  receives 
the  impressions.' 5  Evidently  Plato  had  in  mind  a  sensuous 
ground-work '  of  all  existence.  Besides,  it  would  be  incon- 
ceivable to  reduce  all  things  to  an  incorporeal  essence  or 
mere  space.  Plato,  it  is  true,  characterizes  the  four  elements 
according  to  geometrical  solids  consisting  of  nothing  but 
triangular  surfaces.6  Zeller  points  out  this  latter  Platonic 
theory  as  a  decisive  proof  against  the  theory  of  corporeal 
primary  matter.7  But  when  Plato  maintained  that  '  every 
solid  must  necessarily  be  contained  in  planes ',  he  did 
not  mean  that  they  are  composed  of  planes  and  nothing 
else.  He  did  not  mean  to  reduce  this  solid  world  to  an 
empty  geometrical  structure,  to  a  mere  house  of  cards. 
A  thousand  planes  do  not  make  an  actual  solid.  But  it 
seems  that  Zeller  here  lost  the  thread  of  Plato's  argument. 
Up  to  the  middle  of  p.  $$  Plato  was  discussing  the 
three-fold  classification  of  Being,  and  particularly  the 
material  substrate  of  all  things,  that  indeterminate  mass 
existing  before  the  creation,  in  which  '  fire  and  water  and 
earth  and  air  had  only  certain  faint  traces  of  themselves, 
and  were  altogether  such  as  everything  might  be  expected 
to  be  in  the  absence  of  God  '.8  And  now  Plato  commences 
a  description  of  the  process  of  creation  proper,  the  process 
of  formation  of  the  universe.  I  mean,  putting  form  to 
the  primordial  chaotic  matter  and  unfolding  its  dormant 
elements.9     And  it  is  here  in  the  discussion  of  the  formal 

D  Tim.,  p.  51.  6  Ibid.,  p.  54. 

7  Zeller,  Plato  and  the  Older  Academy,  VII. 

8  Tim.  51. 

9  Nw  5'  ovv  tj\v  8iara£iv  avruv  lmx*ipr)Ttov  kicaaruv  /ecu  "yiveaiv  arj9ei  Xoy<j> 
7rpos  v/xas  SrjKow,  Tim.  53  b  The  word  diataxis  Jowett  translated  by 
'  disposition  ',  which  may  suggest  that  Plato  sets  out  to  discuss  the  essence 


INTRODUCTION  7 

aspect  of  the  universe  that  the  description  of  the  geometrical 
figures  comes.  Thus,  things  were  not  made  of  but  according 
to  plans,  surfaces,  and  space  is  not  the  material  but  the 
formal  cause  of  all  things.10 

To  come  back  to  our  main  discussion,  another  argument 
might  be  presented  in  favour  of  the  materialistic  view  of 
space.  In  describing  the  primordial  receptacle,  the  matter 
of  generation,  he  remarks  'that  if  the  model  is  to  take 
every  variety  of  forms,  then  the  matter  in  which  the  model 
is  fashioned  when  duly  prepared,  must  be  formless,  and 
the  forms  must  come  from  without'  (Tim,,  p.  50).  Now 
it  is  conceived  that  Plato  believed  in  the  primordial 
existence  of  an  absolutely  formless  mass  which  was  in- 
formed from  without  like  the  wax  by  the  seal.  The  modern 
man  can  hardly  conceive  matter  and  form  being  separate : 
this  is  because  his  accumulated  experience  leads  him  to 
be  cautious  in  forming  his  cognitions,  and  not  to  attempt 
to  leap  over  the  circle  of  phenomena.  The  ancients,  on 
the  other  hand,  were  inexperienced,  youthful,  rash,  and 
ready  to  objectify  and  hypostasize  any  idea  that  presented 
itself  to  their  premature  minds.  It  is  only  the  particular- 
istic view  of  mankind,  i.  e.  the  view  of  man  as  separate 

of  things,  but  a  more  faithful  rendering  is  'arrangement',  which  fits  better 
with  the  line  of  argument. 

10  Indeed  it  is  highly  probable  that  even  the  Pythagoreans,  who  held  that 
number  is  the  principle  of  all  things,  did  not  hypostasize  it,  did  not  consider 
it  the  essence  and  substance  of  things,  but  rather  their  formal  element. 
Aristotle,  in  his  Metaph.,  I,  2,  5  ;  XIV,  3  asserts  that  the  Pythagoreans  con- 
sidered numbers  to  be  things  :  and  in  Metaph.,  I,  6  he  remarks  that  they  are 
prototypes  of  things.  Zeller  (see  his  Greek  Philosophy  to  the  time  of  Socrates, 
I,  p.  369)  lays  stress  on  the  first  statement,  and  explains  that  they  are  also 
prototypes  in  the  sense  of  law,  but  many  other  students  of  ancient  philosophy 
support  the  latter  statement  of  Aristotle  to  the  exclusion  of  the  former.  See 
Ritter,  Geschichte  der  alten  Philosophie,  IV,  ch.  2. 


8  PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

individuals,  that  makes  Socrates  and  Plato  ancient ;  a  truer 
view  is  the  general  and  evolutionary  one  which  considers 
John  Locke  and  Immanuel  Kant  as  ancient,  and  Socrates 
and  Plato  as  youths  wantoning  with  abstractions  and  mere 
ideas.  Plato  particularly  had  that  tendency  to  objectify 
and  to  hypostasize  logical  realities.  One  can  therefore 
easily  grasp  Plato's  assumption  of  the  coalescing  of  two  inde- 
pendent elemental  realities,  form  and  matter  thus  producing 
all  things.  But  one  cannot  conceive  how  Plato  would  make 
empty  space  as  the  universal  substratum  and  at  the  same 
time  insist  that  the  form  should  come  from  without.  For 
if  form  here  means  anything,  it  means  certain  limitations 
of  magnitude.  This  body  has  a  cubical  form,  another 
spherical  and  still  another  oval.  But  magnitude  means 
extension,  and  to  speak  of  formless  space  is  to  speak  of 
an  unextended  space  or  of  a  non-spatial  space,  which  is 
absurd.11  And  it  is  equally  absurd  to  insist  on  having  the 
form  come  from  without,  for  by  definition  form  can  come 
from  space  only.1? 

So  much  for  the  corporealistic  view  of  Plato's  conception 
of  space.  On  the  other  hand,  Plato  also  speaks  of  space  in 
a  manner  that  entirely  excludes  all  notions  of  corporeality. 
He  defines  it  in  the  Tim.  52  as  the  'home  for  all  created 
things'.  By  'created  things'  one  naturally  understands 
concrete  objects  composed  of  matter  and  form ;  and  Plato 

11  It  is  impossible  to  evade  the  argument  by  reading  into  Plato  Aristotle's 
definition  of  form,  \6yos  t??s  ovmas.  The  analogies  that  Plato  finds  to  Form 
in  the  seal  impress  on  the  wax  and  in  the  transient  shapes  of  the  gold, 
obviate  such  an  interpretation. 

12  Perhaps  a  similar  objection  can  be  raised  against  formless  matter,  but  we 
must  not  forget  that  the  doctrine  that  extension  constitutes  the  very  essence 
of  material  things  was  not  yet  fully  realized  in  the  days  of  Plato.  The 
Atomists,  for  example,  believed  in  material  atoms  which  were  at  the  same 
time  invisible. 


INTRODUCTION  9 

defines  space  as  outside  of  them,  as  their  home.  Space 
then,  according  to  Plato,  must  be  immaterial.  Further- 
more, he  maintains  that  this  third  nature  'is  eternal,  and 
admits  not  of  destruction'  (p.  52).  Now  in  p.  28  he  had 
laid  down  a  rule  that  '  that  which  is  apprehended  by- 
intelligence  and  reason  is  always  in  the  same  state;  but 
that  which  is  conceived  by  opinion,  with  the  help  of 
sensation,  and  without  reason,  is  always  in  a  process  of 
becoming  and  perishing,  and  never  really  is'.  In  other 
words,  things  material  are  destructible,  and  things 
spiritual  are  eternal ;  and  since  space  is  according  to  Plato 
eternal,  it  cannot  be  corporeal. 

These  are  the  two  views  of  the  Platonic  conception 
of  space,  but  it  seems  to  me  that  either  of  these  two  views 
attaches  itself  to  one  particular  passage  in  the  Titnaens, 
and  does  not  do  full  justice  to  the  argument  as  a  whole. 
It  seems  to  me  that  the  adherent  of  either  view  tears 
passages  out  of  their  context,  and  hence  arrives  at  such 
contradictory  results.  Hence  it  is  of  paramount  importance 
to  analyse  very  carefully  the  whole  development  of  the 
argument.  But  first  let  me  point  out  a  curious  and 
suspicious  contradiction  in  Plato.  First,  it  is  to  be  noticed 
that  from  p.  49  to  p.  52,  where  he  introduced  this  third 
yevos,  this  '  receptacle,  the  matter  of  generation ',  and  where 
he  discusses  it  rather  in  detail,  he  does  not  mention  even 
once  the  word  space  or  its  equivalent  (x<*>Pa>  tottos),  but 
in  p.  52  he  introduces  again  a  third  yivos,  and  there  he 
refers  constantly  to  space  and  no  longer  to  any  'recep- 
tacle'. Is  it  not  curious?  On  further  inspection,  the 
matter  becomes  more  interesting.  In  p.  52  he  describes 
space  as  eternal,  indestructible,  '  perceived  without  the 
help  of  sense,  by  a  kind  of  spurious  reason '.     Now  turn 


lO  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

to  pp.  49-52,  and  here  he  never  mentions  that  the  recep- 
tacle is  eternal.  True,  it  is  spoken  of  as  '  always  the  same ', 
but  the  expression  seems  to  have  a  rather  relative  value. 
It  is  always  the  same  while  the  images  and  the  forms  that 
it  assumes  are  coming  and  going,  transient,  brief,  and 
fleeting.  It  is  the  abiding  groundwork  of  all  transitory 
things.  Yet  he  does  not  say  that  it  is  in  itself,  absolutely 
speaking,  eternal  and  indestructible.  Thus  it  is  strange 
that  the  attribute  of  eternity,  so  emphatically  stated  with 
reference  to  space  (p.  52),  is  entirely  overlooked  in  the  case 
of  the  receptacle  (pp.  49-52). 

The  second  characteristic  of  space,  that  it  is  perceived 
without  the  help  of  sense,  by  a  kind  of  spurious  reason, 
in  a  dreamlike  manner,  is  also  not  clearly  stated  in  the 
case  of  the  receptacle.  He  describes  it  as  '  an  invisible 
and  formless  being',  and  is  'most  comprehensible'  (p.  51), 
and  he  maintains  that  it  is  known  through  a  consideration 
of  the  fleeting  images.  The  meaning  then  is  clear.  We 
cannot  perceive  the  receptacle,  for  it  is  formless.  When 
I  direct  my  gaze  at  the  tree,  I  do  not  see  the  thing  in 
itself,  I  see  the  form  of  the  tree.  Only  its  externality 
is  revealed  to  my  senses.  Sensation  then  has  to  do  with 
the  forms  of  objects,  not  with  the  objects  per  se.  Hence 
one  may  naturally  expect  that  the  receptacle  which 
is  formless  should  not  be  perceptible.  How  then  is  the 
thing  known  ?  The  answer  is  :  the  sensation  of  the  transi- 
tory and  fleeting  object  leads  the  mind  to  assume  an 
abiding  groundwork,  a  receptacle.  Hence  the  latter  is 
known  empirically,  and,  strictly  speaking,  adhering  to  the 
Platonic  terminology,  we  have  no  knowledge  of  space  but 
'right  opinion',  for  every  empirical  cognition  is  a  mere 
opinion.     And  yet,  in  p.  52,  Plato  maintains  that  space  is 


INTRODUCTION  II 

known  by  reason,  though  a  spurious  one,  and  that  it  is  not 
at  all  an  empirical  concept.13 

Thus  the  whole  matter  is  very  puzzling.  Is  Plato  con- 
tradicting himself  in  such  close  juxtaposition,  or  is  the 
receptacle  one  thing  and  space  another?  If  we  now 
proceed  to  a  general  analysis  of  Plato's  argument  in  the 
Timaeus,  I  think  the  puzzle  will  be  solved. 

After  an  invocation  of  the  gods,  Timaeus,  the  natural 
philosopher,  begins  the  story  of  creation.  There  are  two 
natures  in  the  universe,  Being  and  Becoming,  the  permanent 
and  the  mutable,  the  eternal  and  the  destructible.  Every- 
thing that  was  created  has  had  a  design  and  realizes  a 
purpose.  This  idea  is  fully  amplified  and  elaborated  in 
some  detail.  But  this  represents  only  one  view  of  creation, 
namely,  that  of  the  creator.  And  so  at  the  end  of  p.  47  he 
remarks :  '  Thus  far  in  what  we  have  been  saying,  with 
small  exception,  the  works  of  intelligence  have  been  set 
forth  ;  and  now  we  must  place  by  the  side  of  them  the 
things  done  from  necessity,  for  the  creation  is  mixed  and  is 
the  result  of  a  union  of  necessity  and  mind.'  If  by  the 
mind  (vovs)  Plato  understands  the  rational,  and  the  forming 
element,  then  by  necessity  {dvdyKr\)  he  understands  the 
irrational  or  the  plastic  element  in  creation.  By  dvdyKi] 
thus  is  meant  the  motiwi  non  movens,  that  which  receives 
the  free  and  spontaneous  activity  of  the  vovs,  the  mould  or 
the  raw  material  of  creation.  Thus  after  Timaeus  invokes 
the  gods  anew,  he  remarks :  '  This  new  beginning  of  our 
discussion  requires  a  fuller  division  than  the  former.' 
Notice  that  all  he  claims  to  do  here  is  not  to  add  a  new 
nature  of  being,  a  new  genus  overlooked  in  the  previous 

13  On  the  meaning  of  the  '  Spurious  reason '  see  Zeller's  Plato  and  the 
Older  Academy,  VII,  note  60. 


12         PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

discussion,  but  simply  to  give  a  fuller  division.  For  the 
genus  of  Becoming,  before  assumed  to  be  simple,  since  the 
situation  did  not  demand  any  further  analysis,  is  now  to 
be  divided  into  its  constituents  for  the  purpose  of  bringing 
out  the  principle  of  avayKr)  in  the  universe.  Heraclitus 
declared  irdvTa  pe?f  and  Plato  subscribes  to  that  doctrine. 
Yet  it  needs  some  modification.  True  that  the  shape  of 
the  gold  moulded  by  the  goldsmith  is  mutable  and  transi- 
tory, yet  behind  there  is  abiding  gold  that  one  can  point 
his  finger  to  and  say  tovto.  Hence  a  thing  of  Becoming 
is  not  after  all  unique  and  simple,  but  behind  the  fleeting 
forms  there  is  a  more  abiding  substrate.  Becoming,  then, 
can  be  further  classified  into  the  two  incoordinate  elements, 
form  and  matter,  and  the  latter  is  the  principle  of  necessity, 
the  invisible  receptacle  and  nurse  of  generation. 

But  here  (p.  51)  an  epistemological  problem  presented 
itself  before  Plato,  and  he  digresses  for  a  little  while.  If 
we  see  only  forms  and  phenomena,  what  right  have  we  to 
think  of  things  in  themselves,  of  Ideas  ?  And  how  do  we 
know  that  our  mental  representations  have  their  corre- 
sponding objects  in  reality  ?  A  similar  question  might  be 
asked :  How  do  we  know  the  nature  of  the  invisible  raw 
material  ?  But  here  the  answer  is  simple — empirically,  by 
means  of  our  senses.  Fleeting  images  must  have  their 
more  abiding  receptacle.  But  by  what  channel  do  we 
cognize  Being,  the  Ideas  that  are  not  perceptible  to  our 
sense  ?  This  involves  Plato's  whole  theory  of  knowledge. 
There  are  two  different  kinds  of  cognition — mind  and  true 
opinion,  the  former  seeing  things  a  priori,  without  the  aid 
of  the  senses,  and  the  latter  knowing  things  a  posteriori,  by 
experience.  In  correspondence  to  these  two  ways  of  know- 
ledge we  have  the  realm  of  Being  perceived  by  mind,  and 


INTRODUCTION  13 

the  realm  of  Becoming,  including  both  forms  and  matter 
apprehended  by  true  opinion,  which  knows  both  the  image 
and  the  thing.  But  this  twofold  classification  does  not 
exhaust  all  human  cognitions.  It  does  not  include  that 
dream-like  knowledge,  that  mysterious,  inexplicable  '  spuri- 
ous reason  '  which  apprehends  of  a  home  of  all  created 
things,  eternal  and  indestructible.  It  might  be  omitted  in 
the  story  of  the  creation,  for  it  neither  plays  the  creative 
part  of  Being,  nor  is  it  the  plastic  element  of  Becoming, 
but  stands  alone  in  its  eternity  as  the  home  of  all  created 
things,  nay,  as  the  stage  upon  which  the  whole  drama  of 
creation  is  performed,  and  the  stage  never  enters  into  the 
plot  of  the  drama ;  yet  it  cannot  be  overlooked  as  an 
object  of  cognition  in  the  epistomological  discussion. 
Hence  Plato  introduces  here  a  correspondence  to  our  third 
mode  of  apprehension,  a  new  genus,  '  a  third  nature,  which 
is  space'.  After  a  few  remarks  on  the  nature  of  space, 
Plato  returns  (p.  53)  to  the  story  of  creation,  and  having 
discussed  the  material  essence  of  things,  the  universal 
chaotic  mass,  he  now  proceeds  to  tell  how  Demiurgus 
produced  order  and  arrangement  in  the  world,  and  the 
discussion  of  the  material  cause  gives  way  to  the  formal 
cause  in  the  generation  of  the  universe. 

Thus  our  problem  is  solved.  It  was  a  misunderstanding 
that  led  people  to  believe  that  in  the  description  of  the 
receptacle  and  of  space  Plato  referred  to  one  and  the  same 
thing.  We  have  shown  that  on  the  contrary  Plato  conceived 
them  to  be  two  distinct  natures  ;  the  one  partaking  in 
creation,  the  other  containing  creation  ;  the  one  empirically 
apprehended,  and  the  other  independent  of  all  sensations. 
And  all  the  arguments  that  the  supporters  of  the  materialistic 
view  of  space  endeavoured  to  draw  from  Plato's  discussion 


14  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

of  the  receptacle,  the  matter  of  generation,  are  based  on 
a  misunderstanding. 

What  then  are  we  to  gather  from  Plato's  genuine  dis- 
cussion of  space  ?  It  is  not  material,  for  all  material  things 
are  created  and  empirically  given,  while  (p.  38)  space  is 
eternal,  and  beyond  all  experience.  We  derive  the  notion 
of  space  not  from  contact  with  external  reality,  as  the  father 
of  English  empiricism  claimed,  but  it  is  an  innate  idea  of 
the  mind,  that  all  created  things  must  be  in  space.  Psycho- 
logically, this  view  bears  a  striking  resemblance  to  the 
Kantian  conception  of  space,  but  metaphysically  the  two 
are  diametrically  opposed  to  each  other.  Indeed,  according 
to  Plato,  space  is  not  a  mere  ens  rationis,  for  being  eternal 
it  existed  ever  before  the  birth  of  the  human  mind. 

When  we  come  down  from  Plato  to  his  illustrious 
disciple,  Aristotle,  we  feel  somewhat  relieved.  To  be  sure 
the  matter  becomes  more  profound,  the  treatment  more 
analytic,  and  we  have  now  before  us  a  procession  of  brilliant 
syllogisms,  but  the  most  profound  syllogism  may  sometimes 
be  more  easily  digestible  by  the  human  mind  than  the 
smallest  figure  of  speech. 

Aristotle's  Conception  of  Space 

III.  That  place 13a  exists  is  evident  from  our  most  ordi- 
nary experiments.  Watch  a  vessel  through  which  water 
flows  out  and  air  comes  in.  There  has  been  a  thorough 
change  in  the  contents  of  the  vessel,  yet  something  remained 
unchanged,  the  stereometric  content,  the  place,  the  cubic 
inch  or  cubic   foot   which   does    not  change   whether   it 

13 a  It  is  to  be  noted  at  the  outset  that  our  usual  distinction  between 
1  place '  and  '  space '  does  not  exist  for  Aristotle.     They  are  both  identical. 


INTRODUCTION  15 

contains  air  or  water  or  any  other  material.  Thus  place 
evidently  exists.  And  it  has  not  only  mere  existence,  but 
also  different  qualitative  determination,  namely,  upward 
and  downward;  fire  tends  upward,  and  earth  downward 
(Aristotle's  AchtBiicher  Physik,  Prantl,  IV,  ch.  i).  But  what 
is  the  essence  of  space  ?  Here  a  multitude  of  difficulties 
present  themselves.  We  all  know,  of  course,  that  it  is 
characterized  by  three  dimensions.  But  in  what  category 
is  place  to  be  put?  It  cannot  be  matter,  for  in  that 
case  we  could  not  have  a  body  in  space  without  violating 
the  law  of  impenetrability,  according  to  which  two  bodies 
cannot  occupy  the  same  place  at  the  same  time.  For  if 
a  body  could  absorb  another  equal  body,  it  might  go  on 
with  this  process  of  absorption  to  such  an  extent  that 
a  drop  of  water  might  absorb  the  whole  sea  (IV,  8).  Place 
then  cannot  be  material,  for  then  it  could  not  form  the 
receptacle  for  any  material  thing.  On  the  other  hand,  it 
cannot  be  incorporeal  for  it  has  magnitude.  Or  is  it  perhaps 
the  limits  or  the  superficies  of  any  body  ?  Resuming  our 
original  experiment  with  the  vessel,  we  find  that  while  the 
superficies  of  water  make  way  for  the  superficies  of  air,  and 
these  in  turn  make  way  for  some  other  superficies,  what 
we  call  space  does  not  change,  hence  space  cannot  mean 
superficies. 

Thus  we  have  seen  that  space  is  neither  matter,  nor 
form,  i.e.  the  superficies  of  matter.  Indeed,  matter  and 
form  are  internal  in  any  given  body,  while  by  space  we 
commonly  understand  an  external  receptacle.  For  the 
same  reason  we  cannot  maintain  that  space  is  the  interval 
between  the  superficies  of  an  object ;  for  an  object  may 
be  taken  out  of  its  place  and  restored  to  it,  but  one  cannot 
remove  an  object  from  its  interval.     Moreover,  the  identi- 


16         PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

fication  of  space  with  the  interval  of  a  thing  will  lead  us 
into  many  absurdities. 

In  the  first  place,  if  by  space  we  understand  the  interval 
pervading  the  water  or  the  air  passing  through  the  vessel, 
then  every  particle  of  the  moving  body  will  be  surrounded 
by  a  space,  and  consequently  there  will  be  an  infinite 
number  of  spaces. 

Secondly,  a  moving  body  moves  in  space,  but  the  body 
contains  in  itself  a  space  in  the  form  of  an  interval.  Hence 
space  will  move  in  space,  which  is  absurd. 

Thirdly,  when  the  vessel  which  contains  an  interval 
moves  and  occupies  another  interval,  we  will  have  a  fusion 
of  two  intervals  or  spaces,  which  is  likewise  absurd. 

But  if  space  is  neither  matter  nor  form,  nor  the  interval 
of  a  thing,  there  remains  only  one  more  alternative,  and 
that  is  the  adjacent  boundary  of  the  containing  body. 
Man,  we  say,  is  in  the  world  by  virtue  of  his  being  on 
the  earth,  and  on  the  earth  because  of  the  limited  area 
which  closely  comprises  him.  Thus  by  space  we  must 
understand  nothing  else  than  that  which  contains,  i.  e.  the 
vessel  of  any  given  thing.  The  place  of  the  sailor  is  in 
the  boat,  the  boat  is  in  the  river,  and  the  river  is  in  the 
river-bed.  But  Aristotle  is  anxious  to  make  of  space  an 
ultimate  being,  and  hence  maintains  that  strictly  speaking 
space  is  not  the  boat,  nor  the  river,  for  these  are  movable, 
and  a  movable  space  would  signify  a  space  moving  in 
space,  which  is  absurd.  True  space  then  is  immovable. 
It  is  the  extreme  limit  of  the  heavenly  sphere  in  which 
all  things  move,  but  it  is  not  itself  moved.  Consequently 
only  that  is  essentially  in  space  which  is  contiguously 
contained  in  that  extreme  immovable  boundary.  All  other 
things  are  only  accidentally  so  by  virtue  of  their  being 


INTRODUCTION  17 

a  part  of  that  which  is  essentially  in  space,  just  as  we  say, 
reason  is  in  man,  though  strictly  speaking  it  is  only  in 
the  mind  of  man. 

So  far  we  have  been  discussing  space  as  filled  by  this 
or  that  object,  as  irXeov,  but  there  are  some  who  believe 
in  the  existence  of  a  kzvov,  of  pure  and  empty  space 
unoccupied  by  any  material  being,  whether  earth,  water, 
or  air,  a  mere  void,  an  absolute  vacuum.  And  they  support 
their  belief  with  the  following  arguments.  Motion  is 
possible  only  through  a  vacuum  ;  for  if  a  body  could  move 
through  and  penetrate  another  body,  a  sea,  as  we  have 
seen  before,  might  be  absorbed  in  a  drop  of  water.  And 
how  could  any  absorbent  material  soak  into  itself  any 
liquid  without  exhibiting  any  voluminous  increase,  if  not 
for  the  intervening  voids  ?  Aristotle  repudiates  the  exist- 
ence of  any  vacuum.  Attacking  the  argument  from  motion, 
he  maintains  that  motion  is  rendered  possible,  not  neces- 
sarily through  a  vacuum,  but  also  through  an  exchange  of 
places  with  another  body.  Similarly  when  an  absorbent 
body  attracts  a  liquid,  it  may  not  be  because  of  inherent 
voids,  but  because  it  dispels  another  body,  namely,  air. 
Furthermore,  the  fact  is  that  vacuum,  far  from  helping  a 
moving  body,  far  from  forming  the  sine  qua  non  of  motion, 
makes  indeed  the  phenomenon  of  a  moving  body  im- 
possible. Let  us  first  analyse  the  kinds  of  motion.  There 
is  a  motion  of  fire  upward,  or  of  earth  downward,  i.e. 
natural  motion;  and  there  is  a  motion  of  the  ball  that 
has  been  cast,  i.  e.  violent  motion.  Both  kinds  of  motion 
are  impossible,  according  to  Aristotle,  in  a  void. 

The  upward  tendency  of  fire  is  possible  only  through 
the  difference  in  the  conditions  of  the  place  in  which  it 
tends,  from  the  conditions  of  place  to  which  it  tends,  but 
EF.  C 


l8         PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

a  void  cannot  have  these  differences,  inasmuch  as  it  is  the 
privation  of  any  properties  or  conditions.  Hence  natural 
motion  in  a  vacuum  is  an  impossibility. 

Violent  motion  is  similarly  impossible  in  a  void.  For 
the  projected  ball,  according  to  Aristotle,  moves  on  by 
the  impulse  of  the  air  behind,  which  being  lighter  tends 
to  move  faster  than  the  ball ;  but  in  a  void  there  is  no 
air  to  keep  the  ball  in  motion.  Furthermore,  the  velocity 
of  any  given  body  depends  on  the  density  of  the  medium 
and  the  weight  of  the  body.  All  other  things  being  equal, 
the  rarer  the  medium,  the  quicker  the  velocity;  the  less 
the  density  of  a  medium,  the  less  the  time  that  it  will 
take  a  body  to  move  over  a  given  space.  And  since  the 
density  of  a  vacuum  is  zero,  the  time  in  which  a  body 
undertakes  to  pass  over  a  given  distance  will  likewise  be 
zero ;  that  is  to  say,  a  body  will  move  in  a  vacuum  in 
no  time,  which  is  absurd.  A  similar  '  absurdity '  is  reached 
when  we  consider  the  other  determinant  in  a  moving  body, 
namely,  its  weight.  The  weight  of  a  body  is  its  power 
to  cut  its  way  through  a  given  medium,  but  inasmuch 
as  a  void  is  the  absence  of  any  medium,  all  bodies,  whether 
light  or  heavy,  would  fall  with  the  same  velocity,  and 
according  to  Aristotle  this  again  is  absurd.  Consequently 
motion,  in  any  of  its  forms,  would  be  an  utter  impossibility 
in  a  vacuum. 

Or  consider  the  void  in  which  a  body  is  placed.  When 
a  body  is  immersed  in  any  liquid,  the  latter  will  either 
be  compressed  or  displaced  and  dispelled.  But  it  is  in- 
conceivable how  a  void,  sheer  nothingness,  can  either  be 
compressed  or  dispelled.  Evidently  then  the  void  will 
absorb  into  itself  the  immersed  body.  Now  every  body 
possesses  magnitude ;  and  if  the  void  is  real,  how  will  one 


INTRODUCTION  19 

magnitude  absorb  another  one  without  violating  the  law 
of  impenetrability.  Consequently  Aristotle  concludes  a 
void  does  not  exist.  It  should,  however,  be  remarked  that 
the  argument  is  not  altogether  sound.  The  hypothetical 
reality  of  the  void  is  not  consistently  maintained  in  this 
argument.  In  the  first  part  Aristotle  argues  that  the  void, 
even  if  real,  cannot  be  compressed  or  dispelled,  because 
materially  it  is  mere  nothingness,  yet  in  the  latter  part 
he  argues  that  if  the  void  be  real  it  would  absorb  the 
immersed  body  and  thus  violate  the  law  of  impenetrability  ; 
but  if  its  reality  is  not  meant  to  be  material,  we  have  no 
case  here  of  absorption,  or  any  one  body  penetrating  another. 

How  then  does  Aristotle  explain  the  phenomenon  of 
compression  and  condensation  which  is  very  often  adduced 
as  an  argument  in  favour  of  the  vacuum  theory?  And 
what  constitutes  the  differences  between  a  rare  and  a  thick 
body  ?  Is  it  not  that  the  rare  has  many  more  intervening 
voids  which  become  stuffed  with  matter  when  the  given 
body  is  undergoing  a  process  of  condensation  ?  No,  ac- 
cording to  Aristotle,  the  difference  between  a  rare  and  a 
thick  body  is  not  that  the  one  consists  of  segregated  tinier 
particles  than  the  other;  in  other  words,  the  difference 
is  not  quantitative,  but  purely  qualitative.  Matter  is  never 
broken  up  or  discrete,  it  is  continuous  and  unique;  but 
there  are  two  states  of  matter,  the  rare  and  the  thick. 
And  these  two  qualitative  states  are  not  mutually  exclusive, 
but  each  one  harbours  the  potentiality  of  the  other.  Thus 
condensation  and  rarefaction  really  fall  into  Aristotle's 
conception  of  motion,  inasmuch  as  they  are  both  pro- 
cesses of  realization  of  latent  potentialities. 

Let  us  now  formulate  briefly  Aristotle's  main  thesis  in 
the  problem  of  space.   The  term  '  space '  conveys  to  us  three 

C  2 


20  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

distinct  ideas :  either  the  magnitude  of  any  given  body,  i.  e. 
extension,  or  the  receptacle  of  a  given  body,  i.  e.  its  place, 
or  mere  magnitude  not  filled  with  matter,  i.e.  a  void. 
Now  empirical  space  was  not  at  all  a  problem  for  Aristotle. 
He  combated  the  notion  of  space  as  the  '  interval '  (8id- 
a-Trjfxa)  of  a  given  thing,  but  the  existence  of  the  '  interval ' 
he  never  called  in  question.  The  Cartesian  breach  between 
mind  and  body,  which  led  to  the  famous  Kantian  doctrine 
of  the  subjectivity  of  space,  was  yet  unknown.  The  reality 
of  any  concrete  magnitude  is  not  called  in  question.  As 
to  the  notion  of  place,  according  to  Aristotle,  it  is  nothing 
else  than  the  relation  of  contiguity  subsisting  between  two 
bodies.  It  does  not  represent,  then,  any  entity  of  its  own, 
whether  material  or  spiritual.  It  is  a  relation,  it  is  the  point 
of  contact  between  two  concrete  objects.  Finally,  as  to 
the  void,  this  is  entirely  non-existent,  for  the  reason  that 
since  place  is  simply  the  relation  of  proximity  subsisting 
between  two  things,  there  is  no  room  left  for  mere  extension 
outside  of  any  concrete  object  or  void.  Hence  space  is 
finite,  as  finite  as  the  material  universe  of  which  it  is  an 
expression  of  contiguous  relationship. 

It  should,  however,  be  observed  that  Aristotle  was  not 
consistent  in  this  notion  of  place.  He  argues  that  place  is 
essentially  stable  and  immovable,  for  if  it  were  movable  it 
would  move  in  place,  ergo,  place  would  be  in  place,  which 
is  absurd.  Hence,  only  the  all-containing  diurnal  sphere 
immovable — though  revolving  around  its  own  axis — can  be 
designated  as  essential  place ;  otherwise  we  have  only 
accidental  place.  Now  imagine  I  have  a  coin  in  my  hand, 
and  I  move  my  hand  from  point  A  to  point  B  on  my  desk. 
To  be  sure,  the  place  of  my  hand,  that  is  to  say,  the  relation 
of  proximity  between  my  hand  and  the  point  A  changes, 


INTRODUCTION  21 

but  the  relation  between  the  coin  and  my  hand  does  not 
change.  You  may  imagine  also  that  while  I  move  my 
hand  from  A  to  B  the  coin  undergoes  on  its  own  account 
a  simultaneous  change  of  place-relation ;  but  the  two 
changes  in  place-relation  are  mutually  independent,  since 
point  A  is  not  the  place  of  the  coin.  It  is  meaningless 
therefore  to  speak  of  space  moving  in  space,  if  by  the  latter 
is  meant  merely  a  relation  of  contiguity.  Thus  Aristotle's 
distinction  between  accidental  and  essential  place  is  un- 
warranted. Altogether  one  may  speak  of  an  object  as 
being  in  motion,  in  the  sense  that  the  one  and  the  same 
object  preserving  its  whole  identity  changes  its  environment ; 
but  if  by  place  we  understand  just  this  relation  of  environ- 
ment it  cannot  strictly  speaking  move,  for  its  whole  identity 
is  changed,  and  there  is  not  one  relation  moving,  but  there 
are  as  many  distinct  relations  as  points  of  motion.  It  is 
the  failure  to  realize  this  distinction  between  a  relation  and 
a  thing,  i.e.  between  place  as  relation  and  place  as  objective 
space,  that  makes  the  whole  argument  fallacious. 

Thus  I  have  presented  before  the  reader  two  distinct 
views  of  space,  the  Platonic  and  the  Aristotelian.  The 
first,  as  I  understand  it,  looks  at  the  material  universe  as 
a  small  island  in  the  midst  of  a  vast  infinite  sea  which  we 
call  space.  The  other  takes  no  cognizance  of  imperceptible 
space,  but  apprehends  only  corporeal  things  and  their  rela- 
tions. How  far  Jewish  speculation  was  influenced  by  these 
two  views,  the  subsequent  pages  will  attempt  to  describe. 


CHAPTER  I 
Empirical  Space 

I.  That  extensity  is  an  indispensable  element  in  our 
notion  of  matter  was  never  questioned  by  Jewish  thinkers. 
Yet  the  complementary  idea  that  unextendedness  is  an  indis- 
pensable element  in  our  notion  of  spirit  was  less  fortunate. 
The  line  of  demarcation  between  matter  and  spirit  was  not 
distinctly  drawn  by  some  earlier  Jewish  thinkers.  Sub- 
consciously, however,  they  felt  that  an  absolute  spirit  cannot 
be  conceived  in  terms  of  magnitude.  Hence,  while  the  soul 
is  sometimes  spoken  of  in  words  that  do  not  exclude 
extensity,  it  is  always  emphasized  that  the  deity  is  beyond 
the  category  of  space.  Gradually  the  two  types  of  reality 
were  mutually  divorced,  and  the  principle  soon  acquired 
axiomatic  certainty  that  unextendedness  is  the  distin- 
guishing mark  of  spirit,  just  as  extendedness  is  the 
distinguishing  mark  of  matter.  Let  us  see  how  this  change 
came  about. 

Beginning  with  Saadya  of  Fayum,14  an  author  of  the 
earlier  part  of  the  tenth  century,  we  find  that  he  accords 
to  the  soul  only  an  intermediate  position  between  matter 
and  spirit.  It  is  made  of  a  luminous  stuff  that  is  finer  than 
matter,   though  differing    only  in    degree.15      Hence  the 

14  Saadya  may  be  designated  as  the  author  of  the  first  systematic  pre- 
sentation of  the  philosophy  of  Judaism,  though  by  no  means  the  pioneer 
in  Jewish  mediaeval  speculation.  Mention  is  to  be  made  of  Isaac  Israeli  of 
Kairwan,  a  thinker  of  note,  who  died  one  year  before  the  completion  of  the 
Emunot,  but  whose  philosophical  fame  was  eclipsed  by  his  fame  as  a 
physician.     Cf.  Iggerot  ha-Rambam,  p.  a8,  Leipzig,  1859. 

16  See  Emunot,  ed.  Kitover.     I  have  selected  this  uncritical  edition  for 
reference  because  of  its  being  the  most  accessible.    (A  scholarly  edition  of 
the  Emunot  is  now  being  prepared  by  Dr.  Malter.)     See  also  Horowitz,  Die 
Psychologie  bei  denjudischen  Religions-Philosophen,  I,  28. 
22 


EMPIRICAL   SPACE  23 

problem  of  space  and  spirit  did  not  present  itself  to  Saadya 
in  connexion  with  the  soul.  Perhaps  his  treatment  of  the 
deity,  though  belonging  to  the  realm  of  theology,  will  give 
us  a  better  occasion  to  learn  what  he  thought  of  our  problem. 
We  find  that  Saadya  lays  special  emphasis  on  the  non- 
spatiality  of  God.  By  extensity,  he  says,16  we  mean  two 
things,  first  the  tridimensionality  of  an  object,  and  secondly 
divisibility.  An  indivisible  extensity  is  a  contradiction 
of  terms,  for  by  extensity  we  mean  a  simultaneous  conti- 
nuity of  parts.  Feel  this  book,  you  have  a  sense  of  parts 
outside  and  alongside  of  each  other,  and  you  say  it  is 
extended.  Thus  our  notion  of  the  magnitude  of  an  object 
is  composed  of  the  sense  of  its  tridimensionality,  and  that 
of  the  '  alongsidedness '  of  parts  or  divisibility.  But  God 
cannot  be  said  to  be  either  tridimensional  or  divisible, 
hence  he  is  beyond  extension.  In  another  place n  he 
argues  that  only  the  material  can  be  said  to  occupy  space, 
which  according  to  his  conception  means  to  come  in  contact 
with  another  body.  When  we  say  that  an  object  moves  in 
space  we  mean  that  there  is  always  a  point  of  contact, 
a  limit  between  the  earth  and  the  body  which  encompasses 
it,  namely,  air,  but  we  cannot  perceive  how  the  immaterial 
can  meet  a  material  body.  Hence  God  is  not  in  space. 
Saadya,  it  is  to  be  noticed,  alludes  here  to  the  Aristotelian 
conception  of  space,  i.e.  as  '  the  inner  limit  of  the  containing 
body ',  as  we  shall  see  in  the  sequel ;  but  the  basic  idea  of 
the  argument  is  that  inasmuch  as  by  '  limit '  we  understand 
that  point  where  a  certain  body  ends  and  another  body 
begins,  and  that  alongside  of  that  point  there  is  a  series  of 
points  which  do  not  mark  the  beginning  of  another  body ; 
in  other  words,  since  a  limit  conveys  to  our  mind  a  picture 

16  Ibid.,  p.  96.  «  Ibid.,  p.  99. 


24         PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

of  a  series,  of  a  simultaneous  succession  of  points,  i.  e.  a 
picture  of  an  extended  object,  the  immaterial  therefore 
cannot  have  any  limit,  for  the  spirit  lacks  the  attribute  of 
extension.  Hence,  when  the  prophets  speak  of  '  God  in 
heaven  '  they  use  metaphorical  language,  for  surely  they  do 
not  mean  that  God  extends  over,  and  is  contained  in  the 
heaven. 

But  here  we  meet  with  a  tremendous  problem.  How  can 
we  speak  of  divine  omnipresence  ? 18  Omnipresence  is  the 
attribute  of  a  thing  which  is  here  and  there  and  everywhere, 
and  that  which  has  a  '  here '  and  a  '  there '  has  parts  outside 
and  alongside  of  each  other,  and  is  therefore  extended, 
and  to  assume  a  divine  omnipresence  ought  to  be  as  non- 
sensical as  to  maintain  a  spiritual  extensity  or  an  extended 
spirituality.  Saadya,  however,  is  not  ready  to  relinquish 
this  fundamental  dogma  of  religion.  God,  he  explains,  is 
present  in  the  universe,  as  consciousness  is  in  the  body, 

"  See  Emunot,  p.  102.     «*>{?  ly  D1f?E  ^33  ISSOil  l&JBO  "W  T*0 

nioipon  vn  i^tn  mpe  bs  D"np  id  vb&  »jbd  ?ueo  pn  mp»  rrm 
iraw  ins  imten  p  iavw  jv3i  oniN  k-iu  n*n  ab  vpbn  pa  d*t"ibb 
j6i  nnon  t&  mns  ah  *we>  n^>3  pi?  D-np  ws&rD  oha  own 

pDDn .  By  the  expression  DipO  73  DTlp  "ID  N7,  Saadya  does  not  mean 
that  God  existed  spatially  before  creation,  for  that  would  be  a  flat  con- 
tradiction to  p.  99,  where  he  says  1MW  DIpD  DSN1  H3?  "ID  N?K>  lljn 
D1p£^>  IDN'HS  *Yl3y3  pnj?3,  i-e.  that  God  existed  in  no  space  before 
creation.  There  he  also  maintains  that  even  after  creation  God  must  exist 
in  no  space,  for  else  there  would  be  a  change  in  His  being.  Hence  also  the 
expression  HDD  pn  DlpE  HW  t6t?  "IJ?  DlpO  ^33  WXDil  cannot  refer 
to  any  spatial  existence.  Evidently,  then,  Saadya  means  that  while  God  is 
omnipresent,  he  is  not  at  the  same  time  extended  ;  but  he  does  not  explain 
the  apparent  contradiction.  An  attempt  at  explanation  he  makes  in  the 
commentary  on  the  Book  of  Creation,  IV,  1,  where  he  describes  the  deity  as 
the  consciousness  of  the  universe,  permeating  the  texture  of  the  world  by 
means  of  some  rare  and  luminous  gas.  Comp.  Kohler's  Grundriss  einer 
systematischen  Theologie  des  Judentums,  p.  73. 


EMPIRICAL    SPACE  25 

being  found  all  in  all  and  all  in  every  part ;  and  just  as  the 
soul  maintains  its  material  nature  and  indivisible  integrity- 
while  being  diffused  over  the  body,  so  is  God  in  the 
universe.  Cut  a  limb  off  from  a  living  body,  and  the  soul  is 
not  lessened ;  annihilate  a  half  of  the  universe,  and  the  deity 
is  not  impaired.  This  explanation,  however,  can  scarcely 
be  designated  a  solution.  It  seeks  to  explain  one  difficulty 
by  another  difficulty,  the  difficulty  of  extended  divinity  by 
that  of  extended  consciousness.  Once  you  separate  spirit 
from  extension,  you  will  find  mind  in  space  no  more  intelli- 
gible than  God  in  space.  Saadya,  however,  does  not  stand 
alone  in  the  inability  to  cope  with  this  tremendous  problem. 
The  human  mind  thinks  in  terms  of  the  material  data  of 
human  experience,  it  has  no  other  data.  Hence  we  are 
all  labouring  under  a  difficulty  when  we  attempt  not  merely 
to  say  spirit  but  also  to  conceive  spirit,  whether  mind  or 
God.  It  is  just  as  if  the  man  born  blind  would  attempt  to 
conceive  of  colour.  If,  then,  you  accept  the  Cartesian 
dualistic,  position,  you  must  end  in  sheer  agnosticism  of 
anything  spiritual ;  or  else,  leaving  God  to  the  theologian, 
you  must  maintain  that  the  human  mind  is  not  an  entity 
per  se,  hiding  itself  in  some  recesses  of  our  grey  and  white 
stuff — for  the  very  fact  that  you  speak  of  it  as  located  in 
a  certain  place  spatializes  it — but  that  it  is  a  mere  quality 
of  our  brain-stuff,  just  as  heat  is  the  quality  of  a  certain 
body,  meaning  by  quality  a  certain  state  generated  by 
changes  in  the  relative  position  of  the  atoms.  Similarly 
consciousness  is  a  certain  state  generated  by  changes  in 
the  relative  position  of  the  neural  atoms  under  the  action 
of  external  stimuli.  Thus  following  the  Cartesian  dualism 
to  its  logical  conclusion  we  eventually  land  in  material 
monism.     But  that  seems  to  me  the  only  safe  position  if 


26         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

we  have  no  desire  to  entangle  ourselves  in  the  dilemma  of 
space  and  spirit.  But  this  is  evidently  too  advanced  for 
a  mediaeval  thinker,  and  I  have  permitted  myself  to  digress 
in  order  to  solicit  our  sympathy  for  Saadya  and  those  who 
follow  him  in  their  vain  attempt  to  solve  a  difficulty  which 
still  perplexes  the  human  mind. 

An  advance  in  the  conception  of  spirituality  was  made 
by  Ibn  Gabirol,  who  had  the  fortune  of  having  his  works 
quoted  and  discussed  by  the  leading  men  of  mediaeval 
scholasticism  and  his  name  forgotten.19  He  lays  down 
a  positive  principle  that  anything  simple  and  spiritual  does 
not  occupy  space,  and  does  not  fall  into  the  relation  of 
near  and  far.20  He  goes  beyond  Saadya  in  considering  the 
soul  also  an  absolute  substantia  simplex,  so  that  it  is 
altogether  beyond  the  category  of  space.21  This  uncom- 
promising position  opened  before  its  author  the  wide  chasm 
between  mind  and  body.  If  the  objective  world  is  so 
essentially  unlike  the  subjective  world,  what  is  it  that 
transforms  my  impressions  of  external  stimuli  into  a  mental 
representation  ?  And  what  is  it  that  exchanges  my  purely 
mental  act  of  volition  into  muscular  activity?  Gabirol 
attempts  to  bridge  this  chasm  between  soul  and  body.  He 
finds  in  some  sort  of  vital  force  {spiritus)  a  connecting  link, 

19  Orient.  Lit,  1846,  No.  46,  and  Munk's  Melanges,  p.  1528". 

20  '  Omne  simplex  et  spirituale  locum  non  occupat.'  Fons  Vitae,  p.  153. 
'  Substantia  simplex  non  habet  locum  et  omne  quod  non  habet  locum  essentia 
eius  aeque  distat  ab  omni.'  Ibid.,  p.  156,  on  p.  120,  he  remarks :  '  Sub- 
stantia spiritualis  non  est  terminabilis  essentia  quia  non  est  quanta  nee  finita 
et  quod  fuerit  terminabilis  essentia  eius  essentia  extenditur  et  est  in  omni 
loco ';  but  all  he  wishes  to  emphasize  is,  that  of  the  spirit  one  cannot  say  it 
is  here  and  not  there.     It  has  like  relations  in  all  spaces. 

21  '  Anima  mobilis  est  per  se  non  in  loco,'  p.  83.  For  the  designation  of 
the  soul  as  substantia  simplex  see  Horovitz's  Psychologie,  II,  p.  108,  note  65. 


EMPIRICAL    SPACE  27 

a  '  causal  nexus '  between  the  two  extreme  forms  of  being.22 
The  problem,  however,  still  remains ;  what  is  it  that  unites 
this  causal  nexus  to  either  mind  and  body  ? 

After  Gabirol,  we  find  no  Jewish  philosopher  questioning 
the  non-spatial  nature  of  the  soul.  The  problem  now  was 
how  to  conceive  of  a  non-spatial  nature  located  in  a  certain 
place.  God  is  referred  to  very  often  both  by  Biblical 
writers  as  well  as  by  Talmudical  sages  as  being  in  heaven. 
Similarly  the  soul  has  been  located  by  Aristotle  in  the 
heart,  and  later  by  Galen  in  the  brains.  The  opinion 
has  also  been  ascribed  to  Plato  that  every  man  harbours 
in  himself  three  souls,  each  one  having  its  own  habitation. 
But  how  can  a  purely  spiritual  being  be  in  a  certain  place  ? 
When  we  say  that  the  wine  is  in  the  flask,  we  mean  that 
there  is  a  limit  where  the  wine  ends  and  the  flask  or  the 
walls  of  the  flask  begin.  Strictly  speaking,  then,  the 
22  See  D*n  -npe  in,  3 :    wpHn  nnn  "b)b)  tfeb  ninaj  Pfesffl 

inX3  WD  nnX  pfin  nVl  &6  DnW3.  Compare  the  Tractatus  de  Anima 
attributed  by  Munk  to  Gabirol,  where  we  read  :  '  Simplex  autem  non  potest 
coniungi  spisso  sine  medio  quod  habet  similitudinem  cum  extremis.  Item 
anima  non  apprehendit  sensibilia  per  se  nisi  mediante  spiritu  qui  est  sub- 
stantia sentiens  consimilis  utrisque  extremis  et  est  media  inter  corporeitatem 
sensibilium  et  spiritualitatem  animae  rationalis.'  The  notion  of  ruah  as 
distinct  from  nefesh  was  very  popular  in  mediaeval  Hebrew  literature.  See 
Steinschneider  in  Hakarmel,  187 1,  p.  400.  See  also  The  Book  of  Definitions, 
by  Isaac  Israeli,  the  physician,  published  by  H.  Hirschfeld  in  Stein- 
schneider's  Festschrift,  p.  138 :   rWff\\  IPWT1  |»3  pID  HO  ^KW  M^NB"  DH1 

"0D&W  D^y  Nin  nnn  »a  rotofi  *n»e  rw  prraa  pnan  *a  nnb  a^j 
'  prra  t[vh  napcK>  wi  nvy  *n  mum  ia  pnnci  wrcwi  tfap  w*ptw 

13  pVriDl.  Joseph  ibn  Aknin  seems  to  have  been  conscious  of  these  words 
of  Israeli  when  he  wrote :  nnn  JTIW  tibit  DtM  TW*  WSTtl  BtM  nnn 
DB'jn  rbw  t6  B>Mi"n  ejian  ^3^3  nabno.  See  his  Ethics,  p.  174 
(Sepher  Mussar,  ed.   Bacher,   Berlin,   1910).      Comp.   also  Cosari,  p.  96  : 

iwpw  nipa  *r&3  "b  icax  w  vac  on  nna  ds  "a  nannn  vh  tpwm 
3nSn  irei  nWian  ;v&n  n^nan  bw-q  3ni>n  n^pna  )b. 


28         PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

1  inness '  of  a  thing  implies  a  certain  limit ;  but  a  limit  is 
always  the  end  of  a  series  of  points  that  are  not  limits  ;  in 
other  words,  the  end  of  a  certain  magnitude.  But  God  and 
the  soul  are  now  conceived  to  be  non-magnitudinal ;  how 
can  we  designate  them  as  in  a  certain  place  ?  Surprisingly- 
enough,  the  very  author  of  the  dualism  of  consciousness 
and  extension,  Rene  Descartes,  was  guilty  of  the  same 
fallacy.  He  located  the  soul  in  the  pineal  gland.  We 
already  saw  Saadya  finding  difficulty  in  this  idea.  Judah 
Halevi  explains  it  as  follows:  When  we  speak  of  God 
dwelling  in  heaven,  we  mean  nothing  else  than  that  there 
the  workings  of  the  deity  are  most  clearly  and  directly 
manifested  ;  for  below  the  heavens  it  works  through  natural 
agencies,  and  thus  the  divine  plan  can  be  discerned  only 
indirectly.  This  explanation,  it  should  be  noted,  is  based 
on  the  pre-Newtonian  distinction  between  the  natural 
sublunary  world  and  the  divine  superlunary  world.  Later 
Jewish  philosophers  differed  in  explaining  the  expression  of 
'  God  in  heaven ',  but  they  all  agree  that  it  is  not  to  be 
taken  literally.23  A  similar  explanation  Judah  Halevi 
offers  for  designating  the  soul  as  being  in  the  heart,  because 
the  latter  is  the  most  vital  organ,  the  centre  of  all  blood 
vessels  and  arteries,  and  here  again  we  do  not  mean  exactly 
that  the  soul  is  physically  situated  in  the  heart.24  The 
possibility  of  any  place-relation  between  soul  and  body 
was  further  reduced  ad  absurdum  by  a  younger  contem- 
porary of  Halevi,  namely,  Joseph  ibn  Zaddik.  In  his  little 
work  entitled  Microcosm  25  he  argues :  The  soul  cannot  be 
in   the   body,  for   anything  that  is   in   another  object   is 

28  See  Schechter,  Aspects  of  Rabbinic  Theology,  p.  28  et  seq. 
24  See  Cosari,  ed.  Zefri  no  witch,  Warsaw,  191 1. 
26  See  Microcosm,  ed.  Horovitz,  pp.  33,  36. 


EMPIRICAL    SPACE  29 

corporeal.  Moreover,  if  it  were  in  the  body  it  would  either 
be  centralized  in  one  particular  place,  or  else  extended  all 
over  the  body ;  but  in  the  first  case  the  other  parts  will  be 
soulless  and  dead,  and  in  the  other  case  a  limb  cut  off 
would  be  so  much  of  the  soul  taken  away,  which  contradicts 
our  conception  of  the  integrity  and  indivisibility  of  the 
soul.  But  perhaps  it  is  outside  of  the  body?26  Then 
we  would  have  three  alternatives :  either  the  soul  is  removed 
from  the  body,  or  close  to  the  body  on  one  side,  or  else 
enveloping  the  body  like  a  veil.  Now  the  first  alternative 
is  impossible,  for  how  would  the  body  live  when  not  in 
contact  with  the  soul.  The  second  alternative  is  impossible, 
for  then  the  other  side  not  touched  by  the  soul  would  be 
lifeless;  and  the  third  one  is  equally  impossible,  for  if  it 
embraces  an  extended  body  it  must  itself  be  extended.  It 
must  have  a  certain  magnitude  ;  a  pin-point  cannot  embrace 
a  material  object.  But  the  soul  is  pure  spirit,  and  altogether 
unextended.  Hence  any  conceivable  place-relation  between 
soul  and  body  is  absurd.  And  yet  we  speak  of  a  soul 
animating  the  body ;  consequently  there  must  be  some  inter- 
relation between  them.  How  is  that  relation  to  be  under- 
stood? The  answer  to  this  question  Joseph  ibn  Zaddik 
puts  in  very  vague  and  ambiguous  terms.27     He  speaks  of 

26  Such  a  view  indeed  has  been  maintained  as  early  as  Isaac  Israeli  of 
Kairwan  in  the  above  cited  passage  from  The  Book  of  Definitions :  CSJill 

12  pwtdi  pno  vpib  nspEt?  »am  dsb  son. 

27  |Dp  cbw,  p.  36 :  spa  ab  na  w  laionpnc?  n»»  iN3nn  nam 
pi  -irw  spab  nnspni  -nxa  npi  &n  aba  *pb  rmn  vb\  spas  vb) 
bwa\ , . .  spai>  span  P^n  nmpo  ip£  rarp  inn  m&  span  nspno 
oipo  tax  ib  apo  csan  bit*  span  ncrpo  f*m  \rua»  raa  o  fem 
^3B>.  comp.  P.  31 :  t^san  ti*WMV  piiHn  nw  rohrt  bv  rbp  xh 
W  pwn  wn  ^2N  *Dwa  pan  mnp  rwi  sysam  noann.    it  is 

strange  that  the  vegetative  soul  is  here  altogether  omitted,  although  on  p.  37 


30         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

the  soul  being  finer  than  the  mere  extremities  of  the  body, 
and  adhering  to  it  closer  than  one  part  of  that  body  adheres 
to  another.  But  all  this  should  be  taken  as  a  strong  effort 
to  describe  the  spiritual  nature  of  the  soul  in  the  terms  of 
matter.  And  he  warns  us  not  to  conceive  of  the  interaction 
between  mind  and  body  as  in  any  way  material.  It  is  a 
spiritual  interaction. 

Undoubtedly  the  reader  will  still  be  dissatisfied.  A 
spiritual  mode  of  interaction  will  suit  the  spiritual  agent, 
but  not  the  material  recipient.  The  'causal  nexus 'that 
Gabirol  and  Halevi  found  in  the  vital  force  is  no  longer 
applicable  here.  According  to  Joseph  ibn  Zaddik,  the  vital 
force  itself  is  absolute  spirit  beyond  the  category  of  space,28 

he  speaks  of  all  the  three  souls  as  independent  spiritual  substances  ;  and  on 
p.  29  he  maintains  that,  strictly  speaking,  it  is  just  as  improper  to  locate  the 
vegetative  soul  in  the  liver  as  the  vital  soul  in  the  heart,  for  location  would 
imply  spatiality,  and  hence  corporeality.  This  omission  is  not  merely 
incidental ;  it  agrees  with  another  passage  on  p.  28,  where  the  reasons  why 
the  vital  soul  cannot  unite  with  the  body  unless  the  latter  has  been  already 
penetrated  by  the  vegetative  soul,  is  explained  as  follows :  '  Body  is  dead, 
and  the  vital  soul  is  the  source  of  life  ;  the  first  is  fine  and  the  latter  is  thick 
and  earthly.  Hence  the  body  can  unite  with  the  soul  only  when  already 
filled  with  the  vegetative  soul.'  But  the  question  suggests  itself  quite 
readily  :  How  does  the  vegetative  soul  unite  with  the  dead  and  coarse 
body  ?  And  if  Ibn  Zaddik  meant  to  imply  that  the  vegetative  soul  can  come 
in  contact  with  the  body  because  it  is  near  the  material  order  of  existence, 
how  is  it  to  be  reconciled  with  the  other  statement  that  all  three  souls  are 
spiritual  and  non-spatial  ?  The  contradiction  is  patent,  and  all  we  can  do  in 
this  connexion  is  just  to  point  to  it,  but  not  to  remove  it. 

28  Ibn  Zaddik  does  speak  of  a  nTlH  ("in.  a  vital  force,  but  in  his  psycho- 
logical system  it  is  only  one  of  the  constituent  forces  of  the  vital  soul,  and  is 
therefore  pure  spirit.     Comp.  on  p.  28 :   nNHM   NTI   fWTfl   PMJ1    p   byi 

im  *jTn  D*n  mro  >m  nm  nnrn  nwrao  m  wnw  rvnn  nm 

D^pliya.  The  term  nNlBO,  however,  is  difficult,  suggesting  as  it  does 
that  the  fTTin  nil  is  something  independent  of  the  HTI  B>B3,  which  is  ex- 
pressly repudiated  immediately  by  what  follows.    This  vital  force  seems  to 


EMPIRICAL   SPACE  31 

or  any  other  material  accessories.  It  is  itself  an  extreme 
that  needs  a  connecting  link  to  come  in  touch  with  body. 
We  welcome  his  elimination  of  the  !  causal  nexus '  theory, 
which  does  not  help  the  situation  at  all,  and  is  fraught  with 
logical  difficulties,  but  on  the  other  hand  the  doctrine  of 
direct  spiritual  interaction  leaves  the  problem  still  open  on 
the  side  of  the  material  recipient.  However,  occasionalism 
and  parallelism,  or  any  other  doctrine  invented  for  the 
purpose  of  justifying  the  dualistic  standpoint,  does  not  offer 
a  more  satisfactory  explanation. 

The  dualistic  position  received  its  clearest  formulation 
in  the  Microcosm  of  Joseph  ibn  Zaddik.  It  underwent  no 
modification  or  further  development  in  the  systems  of  the 
Jewish  philosophers  that  the  Middle  Ages  produced  after 
him.  We  are  ready  then  to  formulate  our  first  thesis: 
Absolute  spirit  is  distinguished  from  absolute  matter  in 
that  it  is  altogether  beyond  all  notions  of  spatiality.  I  say 
'  absolute  spirit '  and  '  absolute  matter ',  in  order  to  include 
the  first  mediaeval  thinkers,  who  though  they  entertained 
spatial  notions  regarding  the  soul,  which  was  viewed  as 
a  somewhat  material  essence,  yet  removed  all  magnitudinal 
determinations  from  a  truly  spiritual  essence,  e.g.  God. 
And  if  we  consider  that  they  lived  in  an  age  which  was 
quite  productive  of  queer  mystic  treatises  on  different  ways 
of  measurement  of  the  deity  and  its  various  limbs,  we  will 
be  in  a  position  to  realize  the  whole  significance  of  the 
doctrine  not  only  for  the  history  of  theology,  but  also  for 

be  a  superfluous  appendix  to  his  psychology,  perhaps  under  the  influence 
of  Ibn  Gabirol,  though  in  his  own  system  it  is  altogether  meaningless.    Comp. 

p.  28:  2b  new  »]&non  >p:n  mi  ntwa  n^n  wt\  rrttfi  csjn,  and 

on  p.  29 :  2^3  T&S  D*13  DWtM  ffftfl  PSJn  TY\fl2W,  where  this  vital 
force  is  altogether  omitted. 


32  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

that  of  pure  philosophic  speculation.  At  first  there  was 
only  the  antithesis  of  God  and  corporeality,  with  mind 
occupying  the  middle  ground,  but  the  domain  of  spirit 
gradually  appropriated  all  our  psychic  powers  until  the 
middle  of  the  eleventh  century,  when  strict  dualism  became 
the  standard  view-point  in  Jewish  philosophy,  a  dualism  of 
mind  and  body,  the  latter  being  extended  in  space  and  the 
former  spaceless. 

II.  In  the  preceding  discussion  we  have  reached  the 
conclusion  that  spatiality  is  the  distinguishing  characteristic 
of  the  corporeal  world.  Indeed,  if  you  examine  the  different 
systems  in  Jewish  philosophy  you  will  find  that  they  all 
concur  in  defining  matter  as  that  which  has  three  dimen- 
sions. But  this  definition  raises  a  very  important  problem, 
to  which  we  will  now  direct  our  attention.  Tridimen- 
sionality,  we  all  agree,  is  the  distinctive  feature  of  matter, 
but  does  it  constitute  the  very  essence  of  matter?  Evi- 
dently not :  we  can  conceive  of  tridimensionality  devoid 
of  any  material  object.  You  may  apply  the  air  pump  to 
your  jar  and  thus  remove  the  air  almost  completely,  but 
you  cannot  remove  the  spatiality  which  still  remains  in  the 
jar  in  spite  of  your  efforts.  Obviously  the  space  does  not 
constitute  corporeality.  And  if  we  cannot  say  that  a  body 
is  space,  but  that  a  body  has  space,  the  question  remains 
what  is  body  ?  What  is  it  that  hides  itself  behind  a  veil  of 
tridimensionality  ? 

Before  we  start  our  discussion  of  the  Jewish  view,  how- 
ever, let  us  attempt  to  examine  the  problem  somewhat 
more  closely,  and  get  at  the  real  issue.  Pragmatically,  it 
is  to  be  noted,  the  whole  question  is  meaningless.  Reality 
consists  of  groups  of  sense-impressions  which  we  call  things, 
and  with  which  we  are  constantly  in  relation  and  inter- 


EMPIRICAL    SPACE  33 

action  ;  as  for  things-in-themselves,  we  have  as  little  to  do 
with  them  as  with  the  Man-in-the-moon.  When  the  food  is 
tasty  we  are  satisfied,  but  whether  the  food  per  se  is  tasty 
or  not,  we  never  seem  to  worry.  Or,  to  take  a  nobler 
illustration,  we  rejoice  on  a  bright  summer  day  over  a  vast 
green  lawn,  but  we  are  little  concerned  with  the  possibility 
of  there  being  something  that  is  neither  vast  nor  green  nor 
lawn.  The  pragmatist  then  may  very  well  shrug  his 
shoulders  at  the  quibbling  whether  extensity  is  only  pheno- 
menal or  also  noumenal.  Yet  from  the  standpoint  of  the 
historical  investigator,  who  is  anxious  to  trace  the  links  in 
the  development  of  human  speculation,  even  this  quibbling 
becomes  highly  interesting.  The  problem  is  as  follows  : 
Every  object  presents  itself  to  our  minds  in  a  variety  of 
ways.  The  apple  is  perceived  in  the  form  of  greenness 
of  colour,  roundness  of  shape,  smoothness  of  touch,  and 
sweetness  of  taste.  Now  some  of  these  forms  of  perception, 
like  colour  and  touch  and  taste,  are  undoubtedly  subjective. 
The  apple  in  itself  unperceived  by  the  human  mind  is  devoid 
of  these  secondary  qualities.  We  all  admire  the  beauty  of 
the  rainbow,  but  in  fact  this  beautiful  array  of  colours  is 
a  creation  of  our  visual  apparatus ;  what  we  really  have 
before  us  is  a  mere  variety  of  absolutely  colourless  vibra- 
tions of  ether.  And  now  the  question  is  :  What  of  space  ? 
Is  it  also  a  sense-illusion,  or  is  it  real  ? 

In  the  history  of  general  philosophy  we  find  that 
Aristotle  understood  his  master  to  identify  space  with 
matter.29     Whether  it  was  a  true  understanding  of  Plato 

29  See  Phys.,  IV,  2  Sid  ical  TlKaruv  rf)v  vkrjv  koi  ttjv  x°JPav  ravro  <prjatv 
thai  kv  t<£  li/jtaiw  . .  .  "O/xcus  tov  tottov  ual  rrjv  x^Pav  T°  a^T°  airi^-qvaTo.  See 
Tim.  52  a.  Comp.  Baeumker,  Das  Problem  der  Materie  in  der  griechischen 
Philosophie,  pp.  177  ff. 

EF.  D 


34         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

or  a  misunderstanding,  I  have  attempted  to  decide  in  the 
introduction.  But  mediaeval  thinkers  after  all  followed 
Aristotle,  and  were  consequently  influenced  by  this  ascribed 
Platonic  notion.  A  similar  theory  was  maintained  by 
Descartes,  who  in  his  zeal  to  widen  the  gulf  between  mind 
and  matter,  made  extension  the  essential  nature  of  things, 
and  was  consequently  led  to  deny  the  existence  of  a  void, 
for  a  void  is  abstracted  spatiality,  immaterial  extension, 
which  is  from  the  Cartesian  standpoint  an  absurd  contra- 
diction. We  may  mentally  abstract,  he  argued,  all 
characteristics  by  means  of  which  the  external  world  makes 
itself  known  to  our  senses,  but  we  cannot  abstract  the 
element  of  spatiality  without  destroying  our  cognition. 
We  may  conceive  of  a  colourless,  tasteless,  and  odourless 
object,  but  we  cannot  conceive  it  non-extended.  Hence 
extension  must  be  the  essences  of  an  object,  the  primary 
quality,  unbegotten  by  the  mind  and  independent  of  all 
perception.  The  avalanche  is  none  the  less  big  in  far  off 
arctic  regions  where  there  is  no  human  eye  to  perceive 
its  'bigness'.  Space  is  that  attribute  of  things  without 
which  their  existence  is  utterly  impossible.30 

The  same  argument  that  led  Descartes  to  maintain  the 
absolute  and  unconditioned  reality  of  space,  induced  Kant 
to  uphold  the  ideality  of  space.  If  I  cannot  abstract  the 
space  element  without  destroying  my  cognition  it  does  not 
follow  that  space  is  an  external  reality,  for  that  will  not 
account  for  the  impossibility  of  a  mental  abstraction  of 
spatiality,  but  it  does  follow  that  space  is  the  mental 
condition  and  the  indispensable  framework  for  all  per- 
ception.    Just  as  when  we  look  through  blue  spectacles, 

so  See  Descartes,  Principes,  I,  63-4  ;  II,  H. 


EMPIRICAL    SPACE  35 

we  see  a  world  of  blue,  blue  suns  and  mountains  and  trees, 
so  the  mind,  when  it  turns  its  gaze  on  the  external  world, 
puts  on  spectacles  of  spatiality  and  thus  beholds  a  strange 
extended  universe.  Consequently  things-in-themselves, 
independently  of  our  senses,  are  beyond  the  category  of 
space ;  it  is  the  mind  only  that  envelops  them  in  a  garb 
of  extension  ere  it  admits  them  into  its  own  domain. 

Thus  we  have  three  solutions  to  the  problem  of  space 
and  matter,  each  solution  marking  a  certain  state  of  progress 
in  the  development  of  human  thought.  First,  we  have  the 
pseudo-Platonic  theory  which  maintains  that  space  is  the 
undifferentiated  material  substrate  of  all  things,  the  raw 
material  which  the  architect  moulded  into  the  infinite 
variety  of  things,  the  wax  upon  which  the  great  Demiurgus 
impressed  his  signet.  Secondly,  we  have  the  Cartesian 
solution,  according  to  which  space  is  not  matter,  and  the 
very  ground-work  of  all  things,  but  the  primary  dis- 
tinguishing attribute  of  corporeality,  meaning  by  '  primary ' 
the  only  quality  which  really  adheres  to  an  external 
object  independently  of  human  perception,  and  by  '  dis- 
tinguishing' the  only  quality  without  which  the  existence 
of  corporeality  is  unimaginable.  Finally,  we  have  the 
Kantian  solution,  according  to  which  space  is  neither  matter 
nor  an  unconditional  attribute  of  matter,  but  a  subjective 
form  of  intuition,  a  framework  of  sensibility. 

Now  what  solution  did  the  Jewish  thinkers  offer  to  our 
problem  ?  It  should  be  noted  that  virtually  all  of  them 
define  matter  as  that  which  has  three  dimensions,  some 
even  make  tridimensionality  itself  the  definition  of  matter, 
yet  one  must  be  cautious  in  drawing  from  this,  usually 
careless,  definition  any  conclusion  regarding  the  reality  of 
space.     However,  some  Jewish  thinkers  were  more  explicit 

D  2, 


36         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

on  that  point.  In  his  Emiinot  we-Deotzl  Saadya  illus- 
trates how  one  can  rise  from  reflection  on  the  empirical 
data  of  consciousness  to  the  highest  limit  of  human  under- 
standing, by  first  abstracting  from  any  perceived  body  all 
the  transient  qualities  like  colour,  heat,  etc.,  then  also 
abstracting  the  notions  of  extensity,  and  proceeding  with 
this  method  of  abstraction  until  the  mind  steps  on  the 
threshold  of  pure  substantiality — Kant  would  have  said 
the  noumenon — which  is  beyond  all  human  cognition.  It 
is  evident  then  that  Saadya  considers  spatiality  as  some- 
thing external  to  the  essence  of  substantiality,  as  something 
that  can  be  abstracted  without  destroying  the  concept,  as 
something  purely  accidental.  This  view  of  space  is  strictly 
Aristotelian,  in  which  system  spatiality  is  one  of  the  acci- 
dental categories  of  substance;  and  it  is  also  shared  by 
the  Arabian  school  of  thinkers  going  under  the  name  of 
Brothers  of  Purity.32  In  Jewish  circles  it  was  by  no  means 
the  predominant  one,  yet  it  found  its  adherents  in  Saadya, 
as  already  noted,  in  the  staunch  Aristotelian  Moses 
Maimuni,  and  in  a  number  of  other  thinkers.  Maimonides 
especially  maintained  that  spatiality  does  not  constitute 
substantiality,  that  a  substance  consists  primarily  of  matter 
and  form,  both  of  them  indescribable  in  terms  of  extension 
which  is  only  accidentally  attached  to  them.33  Similarly, 
Samuel  ibn  Tibbon  holds  that  magnitude  is  an  accident 
only,  that  substance  is  conceivable  without  it.34     Indirectly, 

31  See  Emunot,  p.  84. 

32  Dieterici,  Naturansehauung,  p.  29  :  '  Der  Raum  ist  eine  von  den 
Eigenschaften  der  Korper,  er  ist  ein  Accidens,  das  nur  am  Korper  besteht 
und  nur  an  ihm  sich  findet.' 

33  Guide,  I,  76. 

34  Scheyer  in  Das psychologische System  desMaimom'des(Frank{urta.Mam, 
1845,  p.  no)  thinks  that  Ibn  Tibbon  opposes  Maimonides  in  this  regard,  and 


EMPIRICAL    SPACE  37 

from  a  pupil  of  the  famous  astronomer  of  the  University 
•  of  Padua,  Elijah  del  Medigo,  we  learn  that  the  latter  held 
the  same  view.85  Abrabanel36  and  R.  Jehiel  b.  Samuel 
of  Pisa,37  both  authors  of  the  sixteenth  century,  also 
subscribe  to  that  theory  of  space,  according  to  which  it 
does  not  play  an  essential  role  in  our  conception  of  pure 
matter.  Thus,  one  view  of  the  reality  of  space  is  the 
Aristotelian  one.  Extension  does  not  enter  our  notion  of 
corporeality,  though  no  one  assumed  the  existence  of 
unextended  matter.  Snow  is  always  white,  yet  whiteness 
is  by  no  means  the  essence  of  snow ;  so  matter  is  always 
extended,  yet  extensity  is  not  the  essence  of  matter.  It  is 
an  inseparable  accident. 

Over  against  this  view  we  have  one  that  is  more  akin 
to  the  pseudo-Platonic  conception.  It  was  first  voiced  very 
emphatically  by  an  older  contemporary  of  Saadya,  Isaac 

he  cites  as  proof  the  fact  that  the  former  defined  matter  as  that  which  has 
three  dimensions  QH1  D^pm  flth&  k  BPP  *13*T  &3  Mtfl  Dgtfl  TIM 
(K"a  jn  nn)  naai  3rm  TVIN.  But  this  definition,  far  from  bearing 
witness  to  a  substantialistic  theory  of  space,  might  suggest  the  opposite,  for 
it  includes  in  the  make-up  of  matter  something  that  has  tridimensionality 
and  hence  beyond  it.  This  latter  view  is  indeed  explicitly  maintained 
by  Ibn  Tibbon  in  the  tenth  chapter  of  the  same  work,  where  we  read  : 

pi  raxm  annm  i-nun  *a  wewi  nxy^  mpn  twi  nifcan  »a  psd  pw 
ovyn  rinEK  n^tan  pm  iann  ovy  wn  nrefown  nwm  nnnxn 

D¥j£  np»  iriN  "Ol  (Wl  p  DK  NWT.  But  this  passage  was  altogether 
overlooked  by  Scheyer,  and  also  by  Schmiedel,  who  followed  him  blindly. 
(See  his  Studien  iiber  Religwnsphilosophie,Wieii,  1869,  p.  277,  n.  2.)  It  is  also 
noteworthy  that  it  is  by  no  means  certain  that  Samuel  Ibn  Tibbon  is  the 
author  of  the  pamphlet  entitled  Rnah  Hen.  But  the  other  theories  are 
no  less  probable.  At  any  rate  it  is  the  work,  not  the  authorship,  that  is 
important  in  this  connexion. 

35  See  fnan  htttP  niW,  p.  to, 

S6  Ibid.,  p.  20. 

37  See  Minhat  Kenaot,  ed.  Kaufmann  (Berlin,  1898),  p.  37. 


38    PROBLEM  OF  SPACE  IN  JEWISH  PHILOSOPHY 

Israeli,  in  his  statement  that  '  tridimensionality  is  matter, 
and  matter  tridimensionality  \38  Israeli  seems  to  have  held 
this  doctrine,  a  truism,  an  axiom  of  thought  which  requires 
no  proof.  Later  thinkers  were  somewhat  less  confident 
in  this  regard.  Yet  the  conclusions  of  some  of  them  at 
least  were  not  substantially  different.  Gabirol  considers 
all  existence,  both  material  and  spiritual,  essentially  one. 
The  divine  intellect  and  the  mute  rock  are,  according  to 
him,  made  up  of  the  same  matter;  it  is  only  the  form, 
the  differentiating  principle  in  the  universe,  that  made  one 
mute  and  the  other  mental.  The  genesis  of  the  Universe 
was  then  as  follows :  Originally  there  was  the  hyle.  Then 
the  hyle  was  divided  in  two,  one  part  of  which  assumed 
the  form  of  spirituality,  and  the  other  corporeality.  Then 
each  great  division  further  divided  itself,  and  again  sub- 
divided itself,  giving  rise  to  the  infinite  variety  of  things, 
each  step  in  this  great  evolution  being  a  form  to  that  which 
preceded  and  matter  to  that  which  is  to  follow.  If  we 
take  a  flower,  we  may  trace  back  the  different  stages  that 
this  flower  stuff  underwent  on  its  march  from  the  hyle. 
Let  us  consider  the  few  more  conspicuous  stages.39  Our 
first  impression  of  the  flower  is  the  red  colour,  and  we  call 
it  the  quality-form.  But  redness  has  no  existence  per  se. 
What  is  it  that  is  red  ?  You  will  say,  of  course,  the  flower 
is  red.  But  the  flower  nature  is  present  in  each  one  of  its 
minute  particles,  yet  each  minute  particle  is  not  red,  just  as 
each  thin  leaf  of  a  gilt-edged  book  is  not  perceptibly  gilt ; 

38  See  Sefer  Yesodot,  ed.  Fried,  Drohobycz,  1900,  p.  47. 

39  Cf.  Fons  Vitae,  p.  204  :  '  Et  quo  magis  redierit  et  exierit  a  substantia 
ad  quantitatem  et  a  quantitate  ad  figurant  et  a  figura  ad  colorem,  manifestius 
fiet  ei  esse  propter  crassitudinem  suam.'  Notice  the  four  stages  in  the  genesis 
of  all  things  :  (1)  substance,  by  which  is  meant  the  first  matter  ;  (2)  quan- 
tity ;  (3)  shape ;  (4)  colour. 


EMPIRICAL    SPACE  39 

consequently  a  flower  is  red  only  by  means  of  extensity, 
which  stands  in  the  same  relation  to  colour  as  matter  is 
to  form.  Now  analyse  further  and  inquire  what  is  extensity, 
and  what  is  it  that  sustains  it.  Gabirol's  relativism  pre- 
vents him  from  halting  at  extensity,  though  he  identifies 
it  with  corporeality ;  and  hence  he  maintains  that  extensity 
is  the  form  which  combines  with  the  original  undefined 
hylic  matter.  And  even  before  subjecting  itself  to  the 
categories  of  accident,  the  substance  that  the  Greeks  called 
fieragv*0  i.  e.  the  first  compound  of  matter  and  form  was 
already  extended.  Thus  Gabirol's  view  on  our  problem 
is  clear,  though  expressed  in  the  very  vague  and  disputed 
terms  of  matter  and  form.  Extensity  is  not  a  phenomenon 
of  corporeality  like  colour,  sound,  smell,  but  that  of  which 
they  are  phenomena,  that  is  to  say,  corporeality  itself.41 

40  Whether  Aristotle  assumed  a  metaxu  was  one  of  the  issues  in  the 
Neumark-Husik  controversy,  for  which  see  Archiv  fur  Geschichte  der  Philo- 
sophies XXIII,  4,  1910,  and  XXIV,  3,  1911.  It  is  curious,  however,  that 
Isaac  Abrabanel  seems  to  have  foreseen  this  controversy,  and  decided  the  case 
in  favour  of  Husik,  see  }ri3n  TIKIS'  lYl/KB',  p.  20.  Yet  one  is  no  heretic  if 
he  doubts  Abrabanel's  authority  for  Aristotle. 

41  Pons  Vitae,  p.  229  :  '  Sed  vides  quod  materia  corporalis,  i.  e.  quantitas 
quae  sustinet  formam  coloris  et  figurae  non  est  forma  corpori  quod  earn 
sustinet  sicut  qualitas,  i.e.  color  et  figura  est  forma  illi.'  Cf.  also  Guttmann's 
Die  Philosophie  des  Solomon  Ibn  Gabirol,  p.  180.  On  p.  293,  Gabirol  remarks  : 
'  Oportet  ut  scias  quod  qualitas  etsi  adiacet  quantitas,  hoc  non  est  nisi 
quantum  ad  sensum  sed  certe  quantitas  et  qualitas  simul  sunt,  ideo  quod 
color  et  figura  comitantur  corpus  universaliter.'  Gabirol  does  not  mean  to 
imply  that  the  essential  nature  of  extension  is  a  mere  sense-illusion ;  but 
that  though  colour  is  accident  and  quantity  substance,  still  both  are  equally 
necessary  for  the  perfection  of  matter.  The  expression  comitantur  corpus 
is  somewhat  misleading,  but  its  meaning  becomes  evident  on  comparing  the 
Hebrew  Text  of  Palquera  which  reads  yin"1  fftttSti  K1PI  nnDNH  bv  ^28 

(24,  D^n  -npc)  nmn  (i.e.  to  perfect)  rrta£  D^nno  rwsnm  \m  "o. 

Schmiedel  (/.  c.)  here,  again,  overlooked  all  these  passages  and  cites  only  the 
passage  in  Mefrr  Hayyim,  II,  2  :  (i.e.  a  body)  jflnB>  "IDND  VDM  Tn»W31 


40         PROBLEM    OF   SPACE    IN   JEWISH    PHILOSOPHY 

Gabirol,  it  is  true,  posits  in  every  corporeal  object  an 
unextended  hylic  element,  and  in  this  respect  he  dissents 
from  the  pseudo-Platonic  view  which  considers  space  itself 
the  hylic  element ;  but  the  hyle  as  used  by  Plato  denotes 
a  greater  reality — if  the  latter  can  at  all  be  said  to  be 
greater  or  smaller — than  the  hyle  of  Aristotle  and  the 
mediaeval  thinkers,  so  that  the  two  views  are  at  bottom 
one.  For  our  discussion  we  may  eliminate  altogether  the 
mysterious  hyle  which  tends  to  confuse  the  whole  argu- 
ment, and  thus  formulate  Gabirol's  position  as  follows : 
Extendedness  is  the  essence  of  a  thing  or  the  thinghood ; 
all  other  notions  we  have  of  an  object  are  unimportant 
accident.  The  mathematician,  Abraham  b.  Hiyya,  adopted 
a  similar  view,  and  defined  matter  as  tridimensionality  plus 
something,  the  first  term  being  the  form  of  corporeality, 
and  the  second  the  indeterminate  hyle.i2 

The   same   attitude   was  taken  by  the  author  of  the 
Microcosm,  Joseph  Ibn  Zaddik.43     Tridimensionality,  he 

pDyni  2miTl  "pNn,  and  tries  to  find  the  cause  of  the  disagreement  between 
Gabirol  and  Maimonides  as  to  the  reality  of  space  in  their  different  attitudes 
on  a  certain  point  in  the  problem  of  matter  and  form,  but  he  misses  the  real 
problem  at  issue.  Comp.  also  Scheyer's  Psychologisches  System  des  Maimo- 
nides, p.  no. 

42  See  nnn^n  nuin,  p.  2. 

43  His  meaning  is  at  first  glance  not  very  clear  and  consistent.     On  p.  7 
of  the  Microcosm  Joseph    Ibn   Zaddik  says :   V21?   "ItPN   fl&'JOn   TOWI 

Nints>  n^x  niDtwn  mpDD  wm  ab)  najwi  Dvy  ntryai  rwvnn  mra 
nns  bi&  mm  in«n  p  Hai»  vb«»  noin  baa*  rwim  mp»  n^do 
Dinai  -npaV  mroai  n^pa  i-oi  t[bn>  opo  t&ao.   Thus  he  thinks 

that   'filling  space'  is  an  accident.     Now  turn   to  p.  9:    iTll¥n    1K>a?31 

poiym  amm  -j-n^n  tidm  ^ap^  ^  aamo  *pan  \bbn  wya  rvDtwn 
•6s  n  onaran  nB^tpn  o^iaan  ia  lpaneoi  nioiwn  miv  on  nW 
DWi»n  d"&bwi  onpon  nap  ^ap  DipD  n^do  invnai  mpo  ata 

IWYQ.      Here  he  holds  that  tridimensionality  is  the  form  of  matter,  while 


EMPIRICAL   SPACE  41 

asserts,  is  the  form  and  essence  of  corporeality,  which  the 
hyle  assumes  in  the  process  of  actualization ;  yet  impene- 
trability he  maintains  is  a  mere  accident.  An  accident  is 
an  unessential  element  in  the  conception  of  a  thing,  and 
we  can  very  well  conceive  of  a  substance  as  pure  extensity 
without  thinking  of  that  property  by  virtue  of  which  it 
resists  any  body  attempting  to  take  its  place.  In  fact, 
geometrical  bodies  are  not  impenetrable ;  a  thousand 
angles  may  occupy  the  same  space.  And  this  author 
evidently  applies  the  conception  of  ideal  matter  to  real 
matter.  It  is  the  geometrician  who  deals  with  the  ultimate 
essence  of  things,  all  other  scientists  with  mere  accidents. 

A  slightly  divergent  view  was  maintained  by  Abraham 
Ibn  Daud  in  his  work  entitled  The  Exalted  Faith.  This 
author  points  out  that  tridimensionality  is  not  the  essence 
of  matter,  but  an  accident.  Quantity  is  one  of  the  nine 
accidental  categories.  It  is  accidental  because  it  is  not 
permanent  and  immutable.  From  the  same  piece  of  wax — 
let  us  say  ten  cubic  cm.  in  volume — you  can  mould  any 
number  of  objects  with  an  infinite  variety  of  dimensions. 

*  filling  space '  is  accident.    Similarly,  on  p.  13,  where  he  remarks  :  YlDVl  '3 

mctwn  mw  wo^a  Dipo  pme  nvy  xin  ltan  DTfcon  vrwb  varan 

WW  tipD  i6d*B>31  poyni  amm  IIMI  MPIB>.  When  we  examine, 
however,  the  meaning  of  the  expression  '  filling  space '  in  the  first  quotation, 
we  are  led  to  suspect  that  it  corresponds  to  the  idea  of  impenetrability. 
This  is  corroborated  by  a  study  of  this  term  as  used  by  other  authors.  It  is 
similar  to  the  expression  Dlpft  THC  '  occupying  space ' — both  correspond- 
ing to  the  Arabic  .jIk*  J>««~>>  sometimes  used  to  convey  the  sense  of 
impenetrability.  Comp.  Crescas,  Light  0/ God,  p.  14:  "Iftin  *7$Q  WpttW 
DtM3  n^J  DJnn  yJBJ  KW  "n»l  flTD  IWK  WpDfl  IT-ID"1.  Compare  also 
the   Microcosm    itself,    p.  15:    "P31    ICIpD  vhlSD  KUT»  Span  ?3B   »3   y*T 

txpo  inis1?  v'inb  *inx  epa1?  prv  xb  udd  n^o  vspav  \at.    The 

author's  view  then  is  clear.  Extensity  is  the  ultimate  nature  of  matter ; 
impenetrability  is  a  mere  accident.     See  Appendix,  s.  v.  DlpD. 


42         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

You  may  say  that  though  each  one  of  these  moulded 
objects  has  different  dimensions,  yet  they  all  have  the  same 
amount  of  voluminousness,  i.e.  ten  cubic  cm.  But  melt 
this  piece  of  wax  and  you  get  a  different  quantity  altogether. 
Hence,  when  the  geometrician  comes  to  represent  the 
ultimate  essence  of  this  piece  of  wax  and  draws  a  figure 
ten  cubic  cm.  in  volume,  he  is  wrong,  because  the  quantity 
changes,  while  our  notion  of  substantiality  implies  an 
immutable  and  indestructible  nature.  But  if  the  latter  is 
not  to  be  found  in  the  specific  amount  of  extensity,  it  is  to 
be  found  in  the  abstract  notion  of  extensity.44  When  a  gas 
is  condensed  into  a  liquid,  and  that  in  turn  into  a  solid, 
the  quantity  of  extensity  varies  of  course,  yet  they  are  all 
extended  in  the  same  degree.  And  the  essence  of  matter 
is  extensity.  But  does  not  the  compressed  liquid  have  less 
of  extensity  than  the  free  gas  ?  Yes,  but  extensity  as  the 
ultimate  nature  of  things  is  not  to  be  viewed  quantitatively, 
but  qualitatively.  It  is  the  quality  of  matter  to  be  extended 
just  as  it  is  the  quality  of  man  to  live.  And  from  this 
standpoint  a  blade  of  grass  and  a  vast  landscape  exhibit 
the  same  degree  of  the  quality  of  spatiality.  It  is  this 
indivisible  spatiality  which  forms  the  essence  of  matter, 
and  any  question  of  more  and  less  confuses  the  argument 
by  introducing  a  foreign  element,  i.e.  quantitative  spatiality. 
This  view  of  Abraham  Ibn  Daud  was  adopted  by  the 
famous  disciple  of  Maimonides,  Joseph  Ibn  Aknin.45     And 

44  See  Emunah  Ramah,  I,  i,  2. 

46  See  Moritz  Lowy,  Drei  Abhandlungen,  pp.  12,   13 :    n¥»ta   DtMrtK> 

maw  nvn  by  nmnna  D*mi>B>  ntyh?  a  inw  i^sn  "ie>k  rnpaino 
wn  nn  nan  b""\  p»y  wbwm  arm  nnxni  *pw  a^  tfrn^yn  inw 
pbj  ww  mriN  mw  n^na  »nba  rm&>N-i  >^vna  wnMn  nio^in  py. 

(And  here  one  codex  has  the  following  insertion  :    DTll^  ilC^KVI   '•a  b"^ 


EMPIRICAL    SPACE  43 

it  is  strange  that  Don  Isaac  Abrabanel 46  ascribes  this  view 
to  Ibn  Aknin,  and  gives  no  credit  to  Ibn  Daud.  Interesting 
are  the  two  objections  that  Abrabanel  quotes  to  this  pro- 
found view — objections  that  do  not  evince  a  full  grasp  of 
Ibn  Daud's  theory.  One  objection  is  attributed  to  Aver- 
roes,  and  may  be  stated  as  follows  :  Extensity  means  con- 
tinuity; and  when  a  continuous  object  is  broken  up  it 
loses  its  former  continuity ;  hence  extensity  is  itself  tran- 
sient, and  presupposes  another  immutable  essence  which 
we  might  term  substance.  But  this  objection  evidently 
loses  sight  of  the  distinction  between  quantitative  and 
qualitative  space :  when  a  body  is  broken  up,  its  quantitative 
extensity  is  lessened,  but  its  qualitative  extensity  remains 
unchanged.  Strangely  enough,  even  Ibn  Aknin,  who 
follows  Ibn  Daud  in  his  view  on  space  and  matter,  appa- 
rently attempts  to  reconcile  this  view  with  Averroes's 
objection,  and  explains  it  thus:47  True  that  extensity  is 
the  essence  of  matter,  but  it  is  only  the  formal  essence ;  for 

jnonm  nsDinn  »wn  &ap  *a  bywa  on  tpkd  own  rm&  nya 
12b  mpu-in  «r\  m«n  3"n  ^nnn  «h  nowi  xb  ifwfcn  mwm 
nom  spDW  w  nsan  idwdd  mj?e  nbvn  *a  nbvh  . .  tab 
m  rw  im  nipmn  bx  mten  re*  mran  ron  . . .  Trttn  noina 
mpvtri  mm  D^ann^D  oha  OTJOTfli  rtibwn-) 

«  see  jnan  hue*  rotatr,  p.  18 :  ^  nBTi  nn»  nnx  na  ren  *a 
un  rwi  nr»t^  in  D*ip»  on  ttprncnpi  nipnnn  tfn  niDtwn  rhwn 
n?  aaoi  non  iaa  mnn  ibumi  *3nson  6rwn  K*rc  t\w  :wn  ta 
nviT  by  D'anra  b*rnk>  rt«£»  a  WW  "ik>sxk>  nipis?  own  -n: 
maw. 

«  /wrf. :  wx  mpmm  nipmnD  rwta  Draw  notui  m  nxaji 
ikb*  *6  ropanm  nbapn  ny  ns^  wk  wn  bapom  WW  ^P» 
bpon  ran  £apo  "rib  wm  hdd  mm  m-pan  bx  iron  nbp  ny 
ro  inx  ro  K33  ropanm  thw  aits*  v^vi  nsjwn  *rta  nm. 

It  is  strange  that  Averroes  is  not  mentioned. 


44         PROBLEM    OF   SPACE    IN   JEWISH    PHILOSOPHY 

since  it  is  itself  a  variable,  there  must  be  an  external  hylic 
essence  behind  it.  But  there  are  two  fallacies  in  this 
argument.  First,  if  extensity  changes,  it  cannot  be  form 
which  is  coeternal  with  the  hyle ;  secondly,  extensity  quali- 
tatively considered  is  unchanging,  and  there  is  no  difficulty 
at  all.  The  second  objection,  anonymously  quoted,  also 
misses  the  real  point.  How  can  we  conceive  of  extensity 
without  the  notion  of  dimensions  ?  Of  course  it  is  conceiv- 
able, just  as  life  is  conceivable  as  a  quality  without  the 
notion  of  the  quantity  of  its  duration.  Space  as  a  quality 
is  simple  and  indivisible,  and  this  is  the  ultimate  nature  of 
matter  ;  space  as  a  quantit)'  is  composed  and  divisible.  It 
can  be  augmented  and  lessened,  and  is  a  pure  accident  of 
matter. 

It  is  to  be  regretted  that  this  novel  and  profound  view 
of  space  did  not  find  more  adherents  in  Jewish  philosophy. 
Perhaps  it  was  too  advanced  for  the  period.  It  was  one  of 
those  sparks  of  truth  flashing  before  their  time,  soon  for- 
gotten in  the  surrounding  darkness.  After  Aknin,  the  view 
of  Gabirol,  Abraham  bar  Hiyya  and  Joseph  Ibn  Zaddik 
was  resumed  in  its  original  vague  form.  Moses  Narboni,48 
Shem  Tob  b.  Shem  Tob,49  Abraham  Bibago,50  Aaron  of 
Nicomedia,  the  Karaite,51  all  teach  that  space  is  the  ultimate 

48  ibid.,  p.  9  b :  n^x  WDtwn  rnwn  nsf  *a  wian  sarin  *iidn 
ronnan  mwrn  vm  Down  D^aara  *rfean  tfrfopen  ttpmon  iwi 

rnDDJ  N^l  min  Tibl  NVl  1PN.  It  is  not  clear  what  he  meant  by 
'indeterminate  space'  as  form  of  matter,  Abrabanel  (ibid.,  19a)  rightly 
objects  that  form  is  actual,  and  everything  real  and  actual  is  spatially  deter- 
minate. Perhaps  Narboni  also  had  in  mind  the  pure  and  qualitative 
extensity  of  Ibn  Daud. 

49  Ibid.,  p.  10b.  M  Ibid. 

51  See  his  work  called  Es  Hayyim,  ed.  Delitzsch,  Leipzig,  1841,  p.  43: 

p»y  *bi)  arm  »b  -piK  Kin  ipn  n  npnen  'Da  narw  no  nm 


EMPIRICAL    SPACE  45 

form,  the  essence  of  corporeality.  As  no  one  of  them 
added  anything  original  to  the  conception,  they  may  be 
dismissed  without  comment.  The  problem  of  space  and 
the  ultimate  nature  of  matter  did  not  cease  to  perplex  the 
minds  of  thinkers,  and  as  late  as  the  sixteenth  century  we 
find  a  certain  Rabbi  Saul,  a  pupil  of  Elijah  Delmedigo,  still 
groping  his  way,  unable  to  grasp  how  pure  extensity  can 
be  the  material  essence  of  all  things,  turns  to  Don  Isaac 
Abrabanel  to  lead  him  out  of  the  tangle.  Abrabanel 
analyses  the  various  views  and  finally  decides  :  Space  is 
only  an  accident  of  things,  an  unessential  element  in  the 
conception  of  matter. 

Thus,  to  sum  up,  there  are  two  rival  views  in  Jewish 
philosophy  as  to  the  problem  of  the  relation  that  space 
bears  to  matter,  the  Aristotelian  and  the  pseudo-Platonic. 
Some  uphold  the  first  theory  and  maintain  that  space  is 
not  an  essential  nature,  that  we  might  conceive  an  unex- 
tended  book  or  table,  indeed  the  whole  world  of  matter,  in 
a  pin-point.  Others  are  shocked  by  this  view.  If  there  is 
any  matter  at  all,  it  must  be  spatial.  This  is  how  the  mind 
conceives  of  matter  as  distinguished  from  spirit.  The  one 
is  a  res  externa,  the  other  a  res  cogitans.  Thus  while  some 
of  the  adherents  of  the  latter  view,  like  Isaac  Israeli  of 
Kairwan  and  Aaron  of  Nicomedia  the  Karaite,  go  as  far  as 

bv  a'Ki  pdv)  ami  nnw  wn  njum  p»y  ^n  ami  -jiNn  ton  nvvn) 
Dnvn  pa  d'dh  onvn  |»a  D^xyn  bs\  *pa  rbn  noaDin  n^pmn  &K 
spa  bb>  poyi  nnn  tin  nrr  tfpm  'an  )hn  nib  rm  tf»n  vbi 

n»3Di"Q  D^si'  "HEN.  Compare  an  earlier  Karaite  of  the  middle  of  the 
twelfth  century,  Judah  Hadassi,  who  in  his  Eshkol  Hakofer,  ch.  65,  defines 
matter  as  that  which  has  length,  width,  depth,  and  thickness  :  {J^C?  121  ?2 
*p1^3  Spa  Kip  N1H  '21J?1  pioyi  211  "pX  )b,  implying  that  tridimen- 
sionality  needs  yet  another  element,  perhaps,  hardness,  in  order  to 
constitute  matter.     Aaron  evidently  disagrees. 


46         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

imagining  the  world,  stripped  of  its  accidents,  which  are 
superfluous  both  logically  and  ontologically — the  world  in 
its  essential  and  permanent  nature,  a  network  of  fine  lines 
like  telegraph  wires  without  the  poles,  the  meshes  corre- 
sponding to  concrete  objects;  others  do  not  take  such 
a  thoroughgoing  geometrical  view  of  reality,  and  assume 
the  existence  of  some  hylic  nature  filling  the  great  vacuum, 
together  constituting  matter.  This  substantialistic  view  of 
space  is  further  modified  by  Ibn  Daud,  who  is  followed  by 
Ibn  Aknin.  Space  is  the  essence  of  all  things,  not  as 
quantity,  for  then  it  is  a  variable  compound,  and  cannot  be 
therefore  ultimate  reality,  but  the  simple  and  indivisible 
quality  to  be  extended,  which  is  present  in  the  same  degree 
in  the  tiniest  grain  of  sand  and  in  the  unmeasurable  ocean. 

III.  In  the  preceding  discussion  the  reader  was  un- 
doubtedly impressed  by  the  fact  that  while  the  pseudo- 
Platonic  and  the  Aristotelian  or  Cartesian  views  found  their 
representatives  in  Jewish  philosophy,  one  seeks  in  vain  for 
any  traces  of  the  Kantian  doctrine  on  the  subjectivity  of 
space.  This  may  be  a  source  of  disappointment  or  gratifi- 
cation, but  it  is  not  strange.  The  mediaeval  thinkers  were 
not  yet  so  critical  and  distrustful  with  regard  to  their  senses. 
Their  theory  of  knowledge  was  absolute  empiricism.  Why 
should  we  doubt  the  existence  of  a  thing  which  we  may  see 
and  feel  in  various  ways?  Hence  even  those  who  upheld 
the  view  of  the  accidental  nature  of  space,  nevertheless 
agreed  that  it  is  a  characteristic  indispensable — at  least  in 
experience — of  every  material  object.  It  was  with  them 
an  axiom  of  unquestionable  certainty  that  all  existent 
things  are  extended. 

But  this  leads  us  to  another  problem  which  played 
a  very  prominent  role  in  the  history  of  thought.     Suppose 


EMPIRICAL    SPACE  47 

we  take  a  material  object  and  divide  it  and  subdivide  it, 
and  carry  on  this  process  of  subdivision  ad  infinitum.  Of 
course  the  extensity  of  the  thing  will  shrink  and  shrivel, 
but  in  this  process  of  subdivision  are  we  ever  going  to  reach 
a  piece  of  matter  so  infinitely  small  as  to  be  altogether 
unextended  ?  Our  first  thought  answers  :  Yes,  every  process 
must  have  an  end.  But  this  would  contradict  our  previous 
conclusion  that  matter  must  have  magnitude,  unless  of 
course  we  assume  that  in  this  infinite  process  of  division 
matter  together  with  space  is  annihilated — a  very  im- 
probable assumption,  because  it  questions  the  law  of 
indestructibility  of  matter,  which  no  mediaeval  thinker 
would  dare.  Briefly,  the  problem  of  infinite  divisibility  of 
space,  and  hence  also  of  matter,  presents  itself  for  our 
attention. 

The  doctrine  of  infinite  divisibility  is  as  ancient  as 
Aristotle,  and  together  with  all  other  views  of  this  matter, 
it  held  sway  over  human  minds  in  the  Middle  Ages.  But 
the  Mutakallimun,  the  Arabian  theologians  whose  influence 
on  mediaeval  thought  was  not  insignificant  either,  held 
a  different  view  on  this  matter.  They  were  atomists. 
Apparently  it  is  strange  that  a  system  which  was  founded 
by  Democritus,  and  developed  by  modern  scientists  with 
no  other  motive  than  the  removal  of  an  intelligence,  working 
behind  the  veil  of  phenomena,  was  advocated  also  by 
theologians  who  sought  to  bring  the  theological  element 
of  nature  to  the  foreground.  But  really  those  Arabian 
scholastics  were  not  inconsistent  in  this  regard.  The  Greek 
and  the  modern  atomists  considered  the  atoms  ultimate 
realities  unbegotten  and  indestructible,  whereas  according 
to  the  Mutakallimun  atoms  perish,  and  new  atoms  are  born 
at  every  moment.     Along  with  the  atomism  of  space  there 


48         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

is  an  atomism  of  time.  There  is  a  continuous  creation  as 
well  as  a  continuous  destruction  in  the  whole  universe. 
An  angel  of  death  and  an  angel  of  life  walk  arm  in  arm 
in  the  infinite  voids  of  space  and  time.  There  is  nothing 
lasting  two  moments — is  the  favourite  maxim  of  those 
thinkers.  What  then  is  it  that  abides  in  the  midst  of 
the  universal  and  eternal  change  and  decay  ?  Nothing  else 
than  the  Deity — answer  the  Mutakallimun  triumphantly. 
Thus  atomism  is  accorded  a  prominent  place  in  the  theo- 
logical system  of  the  Arabs. 

I  mentioned  the  atomic  theory  as  disputing  the  field 
with  the  Aristotelian  notion  of  infinite  divisibility.  The 
reader  may  not  at  first  realize  the  dispute  between  the  two 
theories.  An  explanatory  word  is  necessary.  Etymo- 
logically,  'atom'  means  indivisible.  But  the  term  'indi- 
visible' is  ambiguous.  The  chemist  seeks  to  know  the 
elements  that  enter  in  the  composition  of  a  certain  piece  of 
matter  and  the  proportion  of  their  reaction,  and  when  he 
gets  at  the  unit  of  reaction,  at  that  tiny  being  which  is  just 
big  enough  to  unite  with  others  and  form  this  visible 
universe,  he  is  satisfied.  He  has  the  atom;  and  indeed, 
chemically,  it  is  no  further  reducible.  The  physicist,  how- 
ever, who  is  interested  not  only  in  its  mode  of  reaction 
upon  others  but  also  in  its  own  independent  nature,  finds 
that  'indivisible'  is  a  misnomer.  Minute  as  it  may  be, 
it  has  magnitude  and  part  out  of  part,  consequently  it  is 
a  composite.  Thus  we  see  that  the  chemical  notion  of 
indivisibility  does  not  conform  to  the  physical  notion. 
Now  the  Mutakallimun  considered  the  atom  indivisible  in 
this  last  physical  sense,  while  the  Greek  and  the  modern 
scientists  use  the  chemical  notion  of  indivisibility.  The 
Moslem   theologians   think  that   matter    is    composed   of 


EMPIRICAL    SPACE  49 

ultimate  particles  indivisible  and  altogether  spaceless  by 
themselves,  forming  space  by  their  combination.  We  see 
now  wherein  Arabian  atomism  opposes  the  Aristotelian 
doctrine  of  infinite  divisibility.  It  maintains  that  if  you 
will  carry  on  your  process  of  division  long  enough,  you  will 
eventually  reach  an  atom  indivisible,  and  filling  no  space  at 
all,  a  mathematical  point. 

Did  Jewish  philosophy  endorse  the  atomistic  doctrine 
of  the  Kalam  ?  Our  answer  is  in  the  negative.  Altogether 
the  Kalam  was  not  a  prevalent  doctrine  among  the  Jewish 
thinkers,  though  it  found  adherents  in  Karaitic  circles ; 52 
but  Arabian  atomism,  as  distinguished  from  the  Greek 
and  modern  type,  was  mainly  rejected.  Abraham  ibn 
Ezra 53  was  the  only  Jewish  thinker  who  favoured  Arabian 
atomism  ;  while,  even  among  the  Karaites,  it  found  an 
early  opponent  in  Judah  Hadassi.54  Thus  Jewish  philo- 
sophy may  be  said  to  be  in  opposition  to  the  atomic  theory, 
and  in  favour  of  the  Aristotelian  doctrine  of  infinite  divisi- 
bility.    Let  us  examine  some  of  its  arguments. 

Already  Isaac  Israeli  of  Kairwan,55  elder  contemporary 
of  Saadya,  devotes  considerable  space  to  the  atomistic 
doctrine  of  finite  divisibility.  He  refers  to  Democritus 
whom  he  misunderstands.  Democritus,  according  to  Israeli, 
maintained  that  matter  is  composed  of  spaceless  atoms, 

62  The  Karaitic  thinkers  were  generally  inclined  towards  the  Kalam. 
Indeed,  they  even  assumed  the  name  of  Mutakallimun.  See  Cosari,  VI,  5. 
The  Rabbanites,  however,  were  usually  Aristotelians.  Comp.  Guide,  ed. 
Munk,  I,  339,  note  1. 

BS  See  Kerem  Hemed,  IV,  a  and  Appendix,  s.  v.  D1pD.  On  the  authenticity 
of  these  fragments  see  Schreiner,  Der  Kalam  in  derjudischen  Literatur,  p.  35. 

5*  See  E$  Hayyim,  ch.  4.      D>3Dn  tib  jTi  ban  iTOT  mn  D^Nl 

'wi  D^p-in  j»  wnan  naann  nvrb.  Comp.  Eshkoi  Hakofer,  P.  65. 

65  See  his  Book  of  Elements,  ed.  Fried  (Drohobycz,  1900),  p.  43. 
EF.  E 


50  PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

or  points.  But  the  union  of  two  points  can  be  conceived 
in  two  ways :  either  the  totality  of  the  one  unites  with  the 
totality  of  the  other,  or  a  part  of  the  one  comes  in  touch 
with  that  of  the  other.  Now  the  first  case  leaves  no 
separation  or  distance  between  the  two  points,  and  hence 
the  result  of  the  synthesis  would  be  a  point,  and  the  second 
case  involves  the  contradiction  of  a  partial  union  of  atoms 
that  are  by  hypothesis  spaceless  and  devoid  of  parts.  For 
by  a  spaceless  object  we  understand  something  which  has 
no  opposite  sides  :  that  point  which  indicates  its  beginning 
also  indicates  its  end.  Consequently  mathematical  points 
can  never  produce  an  extended  object.56  The  underlying 
idea  of  the  second  part  of  the  syllogism,  namely,  that  any 
object  that  has  two  sides,  has  part  out  of  part,  and  is  there- 
fore spatial,  recurs  in  the  works  of  the  second  Israeli 57  and 
of  Aaron  of  Nicomedia.58 

Saadya  also  combats  vigorously  the  conception  of 
mathematical  points  as  the  ultimate  unities  of  extension. 
An  indivisible  atom,  finer  than  any  fine  thing  conceivable, 
almost  a  spiritual  essence,  is  altogether  unintelligible.59 
But  he  also  realizes  the  tremendous  difficulty  connected 
with  the  theory  of  infinite  divisibility.  If  a  body  can  be 
divided  ad  infinitum,  it  must  be  composed  of  infinite 
particles.  Infinite  means  endless,  that  is,  there  is  no  end 
to  the  particles  in  any  given  distance,  great  or  small.  There 
is  a  difficulty  already,  namely,  that  of  a  given  finite  line 
being  infinite,  for  a  line  is  the  sum  of  its  particles.  Let 
us,  however,  overlook  this  ontological  objection  and  ask 
a  simpler  question.     We  constantly  see  before  us  things 

56  This  ingenious  argument  is  drawn  from  Aristotle's  Physics,  VI,  x. 

67  Yesod  Olam,  I,  23. 

58  Es  Hayyim,  p.  7.  M  Etnunot,  p.  63. 


EMPIRICAL    SPACE  51 

moving',  but  how  is  motion  possible  ?  Imagine  a  given  line 
AB  having  infinite  particles,  and  a  point  P  moving  from 
A  to  B.     Now  it  is  absolutely  immaterial 

AP- B 

whether  AB  represents  a  mile  or  a  yard  or  a  fraction  of 
an  inch,  it  is  infinitely  divisible,  and  has  infinite  parts.  And 
the  point  P  must  move  over  one  part  after  another,  one 
after  another ;  and  in  order  to  land  at  B,  it  must  have 
completed  an  infinite  track,  and  reached  the  end  of  an 
endless  series,  which  is  impossible  and  absurd.  It  can  also 
be  shown  that  P  cannot  even  commence  to  move,  for  the 
tiniest  bit  of  the  line  is  infinitely  divisible,  and  P  finds 
before  itself  an  immeasurable  abyss  in  order  to  reach  the 
very  next  point.  All  of  which  goes  to  prove  that  motion  is 
a  mere  illusion,  or  else  the  theory  of  infinite  divisibility 
is  false.60 

The  reader  will  have  recognized  the  paradox  of  Zeno  of 
Elea.  The  difficulty  is  truly  tremendous  to-day  no  less 
than  twenty-five  centuries  ago.  Saadya  states  that  this 
objection  led  some  thinkers  to  reject  the  theory  of  infinite 
divisibility — which  means  to  face  other  difficulties ;  others — 
to  assume  that  the  moving  point  hastens  some  part  of  the 
way  in  order  to  make  up  for  the  infinite — which  is  the 
view  of  the  Najimites ;  and,  as  Schahrastani  remarks,  hasty 
or  slow,  it  must  go  through  an  infinite;61  still  others — to 
maintain  that  time  is  also  infinitely  divisible,  each  infini- 
tesimal space  corresponding  to  an  infinitesimal  time,  and 
altogether  P  moving  over  a  finite  space  in  a  finite  time — 
an  explanation  which  only  intertwines  one  difficulty  with 
another.     Saadya's  own   explanation  is   as  follows.     The 

60  Ibid.,  p.  59.  tl  See  Schahrastani  (Haarbrucker),  I,  56. 

E  2 


52  PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

theory  of  infinite  divisibility  claims  by  no  means  that  there 
is  actually  unlimited  division.  The  fact  is  that  if  we  continue 
to  break  up  a  given  particle  long  enough,  we  eventually 
reach  a  minimum  sensibile,  and  there  our  process  of  division 
must  end.  By  means  of  magnifying  glasses  and  exceed- 
ingly fine  instruments  this  minimum  sensibile  becomes  a 
composite,  and  is  further  divisible ;  the  limit  of  division 
is  pushed  a  little  further,  but  a  limit  there  is  after  all. 
Thus  there  is  no  such  thing  as  infinite  divisibility  as  far  as 
actual  experience  is  concerned.  All  that  is  claimed  is,  that 
the  mind  conceives  no  limit  to  the  possibility  of  dividing 
a  given  body,  for  this  reason  :  that  small  as  an  object  may 
appear  to  our  senses,  we  may  conceive  of  a  microscope  that 
magnifies  the  object  a  hundred-fold,  and  when  the  minimum 
sensibile  is  reached  under  this  lens  we  may  exchange  it 
for  another  that  has  the  power  to  magnify  the  object  a 
thousandfold,  and  number  is  infinite.  Consequently  we 
can  mentally  divide  an  object  ad  infinitum ;  but  only 
mentally,  in  reality  we  sooner  or  later  get  an  ultimate 
empirically  irreducible  unit,  a  minima  pars.  Hence  the 
possibility  of  motion  which  is  a  phenomenon  of  reality.62 

The  explanation  is  by  no  means  clear  and  cogent. 
Chiefly  there  is  this  difficulty.  We  may  fail  to  dissect  an 
object  experimentally  into  an  infinite  number  of  parts,  but 
if  our  reason  for  maintaining  the  theory  of  infinite  divisi- 
bility is  valid — and  Saadya  claims  that  it  is  valid  within 
its  sphere — there  are  in  that  object  an  infinite  number  of 
points  which,  though  empirically  unknown,  the  moving 
body  must  pass  over  successively  until  the  end  of  the 
endless  series  is  reached,  which  is  absurd.  Thus  Zeno's 
paradoxical  ban  on  motion  on  the  basis  of  the  assumption 

62  See  Emunot,  p.  59,  and  compare  Cosari,  p.  183. 


EMPIRICAL    SPACE  53 

of  infinite  divisibility  is  scarcely  removed.  Saadya's  view 
might  suggest  the  existence  of  two  kinds  of  space — one 
perceptual  and  real,  the  other  conceptual  and  ideal;  the 
former  of  a  discrete  nature,  the  latter  continuous  and  in- 
finitely divisible,  so  that  both  our  perception  and  our  reason 
are  unerring  within  their  distinct  spheres ;  but  it  is  highly 
improbable  that  Saadya  would  have  taken  such  a  dualistic 
standpoint.  Briefly,  then,  Saadya  introduced  Zeno's 
paradox  in  Jewish  philosophy,  but  could  not  explain  it 
himself.     This  was  left  for  a  later  thinker. 

A  strong  plea  for  infinite  divisibility  is  found  in  the 
second  book  of  Gabirol's  Fons  Vitae.  Extensity  and 
indivisibility,  he  argues,  are  altogether  two  different  kinds 
of  being,  the  one  is  matter  and  the  other  spirit ;  and  it  is 
impossible  to  reduce  one  kind  of  being  into  an  essentially 
different  one.  Hence  the  impossibility  of  matter  being 
composed  of  indivisible  and  spaceless  atoms,  or,  as  Gabirol 
calls  them,  minimae  partes.™  It  is  not  denied  that  there 
is  a  minima  pars  as  far  as  our  perception  is  concerned.64 
There  is  a  terminus  a  quo  to  human  vision.  We  cannot  see 
very  well  a  magnitude  smaller  than  a  hair's  breadth.  But 
the  visual  limen  is  not  one  for  all  men.  It  is  relative  only  ; 
a  very  keen  eye  may  see  things  entirely  hidden  from  the 
normal  sight.     Our  perceptual  limen  does  not  at  all  empty 

63  Fons  Vitae,  p.  57  :  *  Impossible  est  invenire  partem  quae  non  dividitur,. 
eo  quod  omnes  longitudines  corporis  sunt  divisibles  usque  in  infinitum  et 
necesse  fuit  omnes  longitudines  corporis  esse  divisibiles  usque  infinitum  ideo 
quod  impossibile  est  aliquid  resolvi  in  non  genus  suum  si  enim  proposita  pars 
quantitatis  resolveretur  in  partem  quae  non  dividebatur,  necesse  esset  quod, 
pars  ilia  aut  non  esset  aut  esset  substantia  simplex.'  Comp.  Israeli's  Book  of 
Elements,  pp.  43,  47  ff. 

M  '  Non  est  impossibile  hanc  partem  esse  miniraam  partium  quantum  ad 
sensum  non  in  se.'     lbi<L>  p.  5,6. 


54         PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

the  ontological  existence  of  a  minima  pars.  If  mathe- 
matical points  were  the  ultimate  constituents  of  matter,  the 
whole  world  would  be  no  greater  than  a  mathematical 
point.65  For  the  whole  has  no  other  qualities  than  those 
of  its  parts,  the  qualities  of  which  may  be  magnified  quan- 
titatively, as  ten  burners  will  have  a  greater  heat  capacity 
than  one,  but  the  synthesis  does  not  create  any  new  quali- 
ties. If,  then,  the  constituent  elements  do  not  possess  the 
quality  of  extension,  how  can  their  aggregate  be  extended  ? 
And  if  the  aggregate  is  not  extended  either,  then  we  would 
have  a  case  of  a  whole  being  equal  to  its  part,  contrary  to 
the  well-known  law  that  the  whole  is  greater  than  its  part.66 
This  latter  contention  is  not  very  convincing.  A  part  may 
be  taken  in  the  physical-spatial  sense  like  an  inch  in  a  yard 
of  extensity,  or  in  the  spiritual-spaceless  sense  like  the  will 
in  consciousness.  Obviously  we  may  say  that  volition  is 
a  part  of  our  conscious  life  without  being  forced  to  say  that 
our  consciousness  must  be  quantitatively  greater  than  our 
volition.  As  soon  as  we  ascend  to  the  domain  of  spirit  we 
must  leave  the  whole  category  of  magnitude  behind.  Now, 
adhering  to  Gabirol's  own  standpoint  that  an  indivisible 
unit  must  be  of  a  spiritual  nature,  we  are  not  subjected, 
with  regard  to  the  aggregate  of  such  units,  to  the  physical 
law  that  the  whole  must  be  greater  than  its  part.     Gabirol's 

68  Fons  Vitae,  p.  52  :  '  Similiter  etiam  si  posuerimus  punctum  esse  partem 
corporis  et  corpus  est  compositum  ex  suis  partibus,  hoc  est  punctis  quod  tibi 
videtur ;  necesse  est  ut  totalitas  corporis  non  sit  divisibilis  quoniam  partes 
eius  indivisibiles  sunt.' 

66  Ibid.,  p.  57  :  '  Si  duae  partes  coniunctae  non  fuerint  pars  divisibilis, 
ipsae  duae  tunc  et  pars  una  erunt  aequales  erunt  ergo  duo  aequalia  uni  quod 
est  inconveniens,  similiter  etiam  dicendum  de  tertia  et  quarta  parte,  usque  in 
infinitum.  Sed  si  compositum  ex  omnibus  fuerit  pars  una  non  divisibilis, 
hoc  est,  si  plures  partes  sint  aequales  uni  parti :  ergo  corpus  totius  mundi 
erit  aequale  uni  suarum  partium  quae  est  indivisibilis.' 


EMPIRICAL    SPACE  55 

first  contention,  however,  that  if  the  atoms  are  conceived  to 
lack  the  quality  of  extension,  they  cannot  form  in  their 
aggregate  any  extended  matter,  for  the  synthesis  does  not 
give  rise  to  any  new  qualities,  is  perfectly  valid. 

An  equally  strong  defence  for  the  theory  of  infinite 
divisibility  was  made  by  Maimonides  in  his  Guide.  He 
clings  to  the  Aristotelian  theory  that  a  moving  object  must 
be  divisible,67  that  an  indivisible  object  must  be  immovable 
and  hence  immaterial.  He  shows  the  absurdity  of  the 
view  that  there  is  an  atom  which  does  not  fill  itself  any 
definite  place,  and  yet  somehow  or  other  keeps  an  atom  of 
space  occupied.  The  reader  of  general  history  of  philo- 
sophy will  here  recall  the  Monads  of  Leibniz.  Indeed, 
Munk  has  already  called  attention  to  a  striking  parallel  to 
this  view  of  the  Mutakallimun,  found  in  Leibniz's  Epistolae 
ad  P.  des  Bosses,  where  he  remarks :  '  Substantia  nempe 
simplex  etsi  non  habeat  in  se  extensionem  habet  tamen 
positionem,  quae  est  fundamentum  extensionis.'  Also  one 
of  the  later  Jewish  thinkers,  Joseph  Albo,  defines  the  point 


87  See  Aristotle's  Physics,  VI,  7.  He  derives  this  idea  that  a  movable 
object  must  be  divisible  from  the  conception  of  change  of  which  locomotion 
is  one  type.     Maimonides'  formulation  of  the  whole  doctrine  is  as  follows  : 

no  ba\  mam  nm  torn  P^nno  yjruno  b  nth  p^nno  rorwto  bz 

fe  DJM  WW  -1K>BK  <N  Tib)  JWUrV  t6  p^>niV  Vfo&  (see  Guide,  II, 
prop.  7).  I  did  not  connect,  however,  the  idea  that  motion  implies  divisi- 
bility with  the  similar  idea  of  change,  for  the  reason  that  the  latter  was 
very  much  disputed  both  in  Arabian  as  well  as  in  Jewish  circles.  Some 
forms  of  change  are  apparently  sudden  and  involve  no  divisibility.  Person- 
ally, I  think  that  the  theory  that  a  movable  object  must  be  divisible,  is  not 
dependent  on  the  notion  of  change.  It  can  be  inferred  from  the  Physics,  VI, 
ch.  1,  where  it  is  argued  that  motion  implies  a  front  and  a  back  side  of  the 
moving  body,  and  anything  that  has  two  extremities  is  extended  and  divisible. 
This,  indeed,  is  the  way  that  Aaron  of  Nicomedia  formulates  it :  yyi3]"lD  ?2W 

pi^nn  bp  rroni)  mnso  r\wip  )b  b».    See  Es  tfayyim,  p.  ?. 


56  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

as  beyond  the  category  of  space,  but  having  position.68 
But  how  can  a  thing  exist  in  the  physical  universe,  not  in 
a  space  garb  ?  And  how  does  a  mathematical  point  mono- 
polize a  definite  space  when  it  is  itself  in  no  need  of  it  ? 
'Such  things',  Maimonides  therefore  concludes,  'are  only 
said  ;  they  exist  only  in  words,  not  in  thought,  much  less  in 
reality.' 69  Another  objection  to  the  Mutakallimun's  stand- 
point is  how  could  we  bisect  a  line  composed  of  an  odd 
number  of  atoms.70  One  might  say  that,  since  the  atom 
has  no  magnitude,  it  is  really  of  no  consequence  for  an 
exact  spatial  division  ;  but  strangely  enough,  according  to 
the  Arabian  thinkers,  it  has  a  magnitudinal  value  in  con- 
junction ;  hence  that  side  which  will  own  this  middle  atom 
will  be  more  extended  than  the  other.  Consequently  an 
exact  division  in  this  case  is  impossible.  This  last  argu- 
ment was  also  advanced  by  Maimonides'  imitator,  Aaron 
of  Nicomedia,  the  Karaite,  in  his  work  called  The  Tree  of 
Life?1 

Finally,  the  problem  of  infinite  divisibility  received  a 
new  treatment  in  the  work  entitled  The  Wars  of  God,  by 
the  acute  thinker  Levi  b.  Gerson,  or  Gersonides.  He 
reiterates  the  idea  that  a  thousand  mathematical  points 
could  not  produce  anything  more  than  a  point.72  He 
points  out  that  matter  has  a  property  called  continuity 
{hitdabbekut),  by  virtue  of  which  it  may  be  divided  and 
subdivided  ad  infinitum,  and  the  most  infinitesimal  parts 

68  Dogmas,  p.  124.  Compare,  however,  Isaac  Israeli  in  his  Yesod  Olam, 
I,  ch.  2,  p.  3. 

69  See  Guide,  I,  51.  This  view  of  the  Kalam  is  also  stated  in  the  Karaitic 
work,  The  Tree  of  Life,  p.  13,  comp.  FV.,  65. 

70  Guide,  I,  ch.  73,  third  premise. 

71  See  p.  7. 

n  Milhamot,  Leipzig,  1866,  p.  345. 


EMPIRICAL    SPACE  57 

will  still  be  extended  and  again  continuous,73  a  view  that 
coincides  with  the  Kantian.  But  his  most  original  contri- 
bution to  the  problem  of  infinite  divisibility  is  his  solution 
of  Zeno's  puzzle,  thereby  changing  the  whole  meaning  of 
the  concept.  We  have  seen  how  Saadya  grappled  with 
that  puzzle  and  scarcely  overcame  it ;  we  are  now  to  see 
how  Gersonides,  four  hundred  years  after,  finally  solved  it — 
a  solution  well  worth  serious  consideration  on  the  part  of 
present-day  thinkers.  Perhaps  we  had  better  let  him  talk 
for  himself.  He  has  just  proved  that  the  very  notion  of 
quantity  in  any  of  its  forms,  temporal  or  spatial,  implies 
finitude  and  limitations,  and  he  remarks  : 74  '  Perhaps  some 
one  will  question  the  argument  just  advanced,  saying  that 
there  is  one  phase  of  quantity  suggestive  of  the  infinite, 
namely,  the  fact  that  number  is  infinitely  augmentable  and 
quantity  is  infinitely  divisible;  and  it  is  also  clear  that 
quantity  as  such  is  infinitely  augmentable,  for  it  is  not 
impossible  that  quantity  as  such  should  be  greater  than  the 
universe.  True,  there  is  something  that  prevents  the 
possibility  of  having  matter  larger  than  the  universe, 
namely,  the  fact  that  there  is  no  space  beyond  the  uni- 
verse, as  the  Philosopher  (i.e.  Aristotle)  has  shown ;  but  it 
is  not  impossible  for  matter  as  such.  ..."  Our  .answer  is 
that  it  is  evident  after  a  little  thought  that  this  objection 
is  unable  to  overthrow  our  premise  which  we  have  laid 
down  before,  namely,  that  quantity  as  such  is  of  necessity 
finite,  for  the  nature  of  quantity  necessitates  finitude,  as 
already  explained.  But  the  endlessness  that  we  find  as 
characteristic  of  number  and  extensity  is  not  endlessness  in 
quantity,  but  endlessness  in  the  process  of  division  and  aug- 
mentation.     That  is  to  say,  much  as  you  divide  it,  the 

73  Ibid.,  p.  333,  also  p.  346.  74  Ibid.,  pp.  333-4. 


58         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

capacity  will  still  be  left  for  further  subdivision ;  and  much 
as  you  augment  it,  the  capacity  will  still  be  left  of  further 
augmentation.  Yet  divide  and  augment  as  you  may,  you 
will  always  have  quantitative  finitude,  for  number  does  not 
have  such  power  as  to  change  into  non-number  (i.e.  infinite), 
but  it  does  have  the  power  to  change  into  greater  numbers. 
Thus  it  can  never  turn  into  an  infinite,  for  it  has  been 
already  explained  that  number  is  finite.  The  same  is  true 
of  extensity.  .  .  .  And  from  this  explanation  it  will  become 
clear  that  extensity  has  no  infinite  number  of  parts  whether 
potentially  or  actually,  for  if  it  had  an  infinite  number  of 
parts  potentially  or  actually,  a  great  absurdity  would  follow, 
namely,  that  a  given  finite  extensity  would  be  infinite,  for 
that  which  is  composed  of  an  infinite  number  of  parts  must 
be  infinite  in  extensity,  for  any  one  of  these  potential  parts 
has  of  necessity  some  quantity,  for  extensity  cannot  be 
divided  into  non-extensity  ;  and  it  is  evident  that,  however 
minute  the  extensity  each  one  of  the  infinite  parts  may 
have,  the  whole  will  certainly  be  infinite  in  extensity.  .  .  . 
Hence  what  we  mean  by  saying  that  extensity  is  infinitely 
divisible  is  that  each  part  retains  the  possibility  of  being 
subdivided,  though  the  number  of  parts  always  remains 
finite.' 

This  whole  discussion  involves  Gersonides'  great  con- 
tribution to  the  notion  of  the  infinite — which  will  be 
discussed  in  a  later  chapter.  The  keynote  of  the  argu- 
ment however  is  clear,  namely,  that  infinite  divisibility 
is  not  a  state  but  a  process,  not  an  accomplished  fact ; 
for  it  is  ridiculous  to  speak  of  an  ended  endless  series,  but 
the  unlimited  possibility  of  dividing  and  subdividing 
extensity  into  smaller  extensities.  And  if  one  were  to  live 
thousands  of  years  and  were  constantly  engaged  in  dividing 


EMPIRICAL    SPACE  59 

and  crumbling  a  piece  of  matter,  with  unimaginably  fine 
instruments,  he  would  have  at  the  end  of  that  time  an 
unthinkably  great  number  of  particles  of  course,  but  it 
would  be  a  finite  number  nevertheless.  Prolong  the  life 
of  that  miserable  man,  and  the  world  would  be  enriched 
by  so  many  more  particles,  but  the  sum  total  will  be  finite 
again.  The  number  of  grains  of  sand  on  the  shore  of  the 
sea  is  overwhelming ;  but  it  is  a  definite  and  finite  number. 
It  is  absurd  and  contradictory  to  speak  of  an  existing 
infinite  number.  Infinite  divisibility  denotes  a  process,  but 
not  a  state.  Such  is  the  solution  of  Gersonides.  It  rids 
us  at  once  of  the  haunting  ghost  of  Zeno  which  continued 
to  appear  as  soon  as  we  had  infinite  divisibility  on  our  lips. 
Gersonides  showed  us  how  to  make  of  it  an  intelligible 
theory. 

We  are  now  ready  to  draw  a  line  under  the  first  general 
inquiry  of  our  work.  The  problems  that  so  far  occupied 
our  attention  are  connected  with  the  conception  of  empirical 
space,  i.e.  with  that  part  of  space  which  has  embodied 
itself  in  concrete  tangible  matter,  and  has  become  therefore 
an  object  of  experience.  We  have  seen  how  the  Jewish 
thinkers  never  doubted  the  independent  objective  reality 
of  space  as  presented  to  their  senses.  They  differed  as  to 
its  ontological  importance  in  the  make-up  of  things,  they 
took  issues  as  to  its  accidental  or  substantial  nature,  but  no 
one  questioned  its  independent  existence.  Thus  the  Kantian 
view  of  the  subjectivity  of  space,  which  puts  all  extensity 
at  the  mercy  of  our  senses,  is  far  removed  from  the  Jewish 
standpoint.  Some  thinkers,  we  have  seen,  even  go  to  the 
extreme  in  maintaining  that  space  is  the  sum  and  substance 
of  all  material  existence,  the  substantial  groundwork  of  all 
things.     Perhaps   this  distinctly  empirical   standpoint   is 


60  PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

somewhat  responsible  for  the  general  Jewish  opposition  to 
Arabian  atomism  with  its  assumption  of  a  real  yet  spaceless 
particle  as  the  basis  of  the  material  world.  At  any  rate, 
Jewish  thinkers  all  upheld  the  indestructibility  of  extension 
by  means  of  division,  that  space  is  infinitely  divisible — a 
theory  the  tremendous  difficulties  of  which  were  altogether 
removed  by  Gersonides,  who  showed  that  the  notion  of 
infinite  divisibility  denotes  a  process  rather  than  a  state. 


CHAPTER  II 

Absolute  Space 

The  subject  that  now  presents  itself  for  discussion,  is 
absolute  space,  by  which  I  mean  not  the  space  of  this  or 
that  object  that  is  directly  given  in  our  intuition,  but  the 
one  that  is  the  product  of  a  mental  process  of  abstraction 
and  generalization.  The  former  space  is  concrete  and 
perceptual,  denoting  an  impress  of  the  external  world  upon 
our  senses ;  the  latter  space  is  absolute  and  conceptual, 
denoting  a  reaction  of  the  mind  upon  the  external  world. 
Empirical  space  is  variegated  and  discrete,  manifesting 
itself  in  the  space  of  this  desk  and  that  landscape  and 
those  heavens ;  conceptual  space  is  uniform  and  con- 
tinuous— one  great  continuum  without  bounds.  The 
conception  is  a  difficult  one,  implying  the  absence  of  any 
material  data  to  which  the  human  mind  could  cling:  that 
is  why  it  was  so  often  a  source  of  error  and  confusion. 
Yet  if  you  close  your  eyes  and  think  away  the  walls  of  the 
room  and  the  furniture  in  it ;  and  think  away  the  world 
outside  of  your  room,  the  sun,  the  moon,  and  the  stars ; 
and  think  away  also  the  earth  under  your  feet,  and  the 
very  body  in  which  your  mind  happens  to  reside ;  and 
think  only  of  your  mind  floating  in  an  endless  monotonous 
void — you   will  have    some  faint  glimpse   of  the  endless 


62         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

continuum  in  which  the  material  universe  is  conceived  to 
be  submerged,  absolute  space. 

We  have  seen  in  the  preceding  chapter  that  Jewish 
mediaeval  thinkers  never  questioned  the  reality  of  the 
extensity  of  things,  never  doubted  the  independent,  objective 
existence  of  empirical  space ;  yet  up  till  the  end  of  the 
fourteenth  century  they  all  unanimously  repudiated  the 
assumption  of  absolute  space.  This  can  be  explained  in 
two  ways.  First  of  all  empiricism  was  the  standpoint 
taken  by  the  Jewish  philosophers  in  the  middle  ages.  It  is 
proclaimed  by  Saadya  in  the  introduction  to  his  book 
called  Beliefs  and  Opinions,  and  it  is  emphasized  by  the 
thinkers  that  came  after  him.  Maimonides  scoffs  at  the 
Mutakallimun,  those  Arabian  scholastics,  who  would  assume 
anything  imaginable  which  would  fit  in  the  system ;  and 
if  contradicted  by  our  senses,  they  would  have  a  ready 
reply:  human  perception  is  not  reliable.75  Hence  this 
empirical  standpoint  might  have  prevented  the  Jewish 
thinkers  from  believing  the  existence  of  anything  that 
cannot  be  empirically  known.  But  there  is  also  another 
reason  that  has  an  equal  degree  of  probability.  Aristotle's 
conception  of  space  was  such  as  to  exclude  the  notion  of 
absolute  space.  Now  Aristotelianism  exercised  unimagin- 
able sway  over  the  Jewish  thinkers.  It  was  the  standard 
of  truth.  Thus  if  the  Bible  took  issues  with  Aristotle,  it 
was  incumbent  upon  them  to  explain  away  the  apparent 
meaning  of  the  Bible,  and  so  interpret  it  as  to  be  in  accord 
with  Aristotle.  '  Stultum  est  dicere  Aristotelem  errasse.' 
Hence  in  accepting  the  Aristotelian  notion  of  space,  which, 
as  I  say,  excluded  the  reality  of  absolute  space,  they  had 

76  Comp.  Guide,  I,  ch.  73,  prop.  10. 


ABSOLUTE    SPACE  63 

to  accept  also  the  conclusion  that  might  be  logically  drawn 
therefrom.  And  so  the  situation  lasted  until  the  Aristo- 
telian influence  began  to  wane,  and  the  great  challenger 
of  Aristotle,  Hasdai  Crescas,  appeared,  and  gave  to  the 
notion  of  space  a  different  meaning,  and  proved  the  objec- 
tive reality  of  absolute  space.  Let  us  first  discuss  the 
history  of  the  Aristotelian  notion  of  space  in  Jewish  philo- 
sophy, we  will  then  come  to  the  objective  reality  of  that 
vast  continuum  which  we  cannot  experience,  but  which  the 
mind  postulates. 

I.  Just  a  word  is  necessary  to  call  up  in  the  reader's 
mind  this  Aristotelian  notion  which  we  have  already  dis- 
cussed in  the  introduction  at  length.  We  all  speak  of 
things  being  in  space ;  the  desk,  the  house,  the  aeroplane, 
the  world— all  things  are  in  space.  Space  then  carries  the 
notion  of  an  encompassing  body,  and  Aristotle  defined  it 
as  the  first  limit  of  the  containing  body.  Now  the  far- 
reaching  consequences  of  this  definition  lie  in  the  fact  that 
it  does  away  with  the  mysterious  independent  existence 
of  space.  It  is  simply  the  relation  of  contiguity  between 
two  objects ;  where  this  contiguity  is  missing,  of  course  you 
have  no  space.  Thus  the  uppermost,  all-encompassing 
sphere  in  the  Ptolemaic  astronomy,  while  being  the  space 
of  all  things,  is  itself  in  no  space;  for  there  is  nothing 
higher  to  be  in  contact  with  it,  not  even  a  void. 

This  Aristotelian  notion  was,  as  I  said,  accepted  without 
reserve.     Saadya76  combats  the  view  of  space  as  that  in 

76  Entunot,  I,  4  :   >Tn  13*1  TO  «M  lONM  pNH  U)p122  niBW  N»tJ>  IN 

vnnm  .mp»n  Tto  intaD  iton  wao  men  to  noNDi  wn  mp»n 
nip»  itrsj  cp^ni  onnnn  nnn  db>id  mn»  no  Rtfi  Dipon  pw  <3 
nnox  »a  in:ink>  ynat\  ;*j«a  rrm  n*fan  rub  pw  nani  Dip»i> 
Nnp>i  ow»n»n  owan  w  tomb  nvi  bin  ntrntr  i»a  wn  mpcn 


64  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

which  all  things  are  submerged,  and  defines  it  as  'the 
contiguity  between  two  objects '.  He  thus  answers  the 
objection  levelled  at  the  adherents  of  the  doctrine  of  creatio 
ex  nikilo,  namely,  what  was  there  in  the  space  of  the  world 
before  it  had  been  created?  Since  there  was  no  world, 
there  was  no  relation  of  contiguity,  and  hence  no  space. 
He  also  meets  Zeno's  argument  that  if  all  things  are  in 
space,  space  itself  will  have  to  be  in  space,  and  so  on  ad 
infinitum,  consequently  space  does  not  exist.  The  strength 
of  this  argument  is  evidently  questionable  ;  all  it  may  prove 
is  that  space  is  infinite,  but  not  that  it  is  non-existent.  To 
Saadya,  however,  such  a  conclusion  would  not  be  in  accord 
with  Aristotelianism,  and  hence  wrong.     He  shows  that  if 

nny  f\^rw  ,1-01-6  mp»  one  nnx  ^  iw  bin  oipo  dkwo  Dipo 
buy  mm  vb)  px  rvnn  si>  iBwai  nn*pi>  mpo  nnvp  naaoa 
D^a  mea  mpo  idk^. 

Kaufmann  in  his  Attributenlehre ,  p.  63,  note  117,  misconstrued  the  whole 
passage.  He  explains  the  phrase  Q<imn  Jinn  Dt^D  NIH^  TfO,  which  he 
wrongly  designates  as  Saadya's  own  view — as  '  dasjenige  was  an  die  Stelle 
der  Dinge  sich  setzt,  d.h.  beim  FortrUcken  eines  Dings  dafiir  eintritt'. 
When  an  immersed  body,  a  cubic  inch  in  volume,  is  removed,  the  liquid  will 
naturally  fill  the  gap,  the  cubic  inch  of  the  liquid  being  the  space  of  the 
displaced  body.  But  according  to  this  interpretation,  an  object  and  its  space 
cannot  be  conceived  simultaneously ;  which  is  absurd.  To  place  an  object 
and  to  displace  it,  are  two  distinct  ideas.  Perhaps  what  Kaufmann  had  in 
mind  is  not  the  cubic  inch  of  the  displacing  liquid,  but  the  cubic  inch  as  such, 
the  stereometric  content,  so  that  the  interval  between  the  superficies  of  an 
object  would  be  its  space,  a  theory  discussed  and  combated  in  Aristotle's 
Physics ;  but  this  '  interval '  is  altogether  wanting  in  the  words  of  the 
definition.  What  Saadya  referred  to  in  that  expression  is  undoubtedly  the 
Platonic  notion  of  an  all-containing  receptacle,  against  which  Saadya 
advances  Zeno's  argument  that  this  receptacle  must  itself  be  contained,  and 
so  ad  infinitum.  Kaufmann  also  misunderstood  the  expression  3HJ*  P3K 
1"Qr6  DlpD  DnO  ir\H  ?3,  apparently  he  read  2W),  for  he  translates  it : 
1  Die  Ausdehnung — eigentlich  das  von  jedem  vonbeiden  Bewohnte ',  but  the 
Arabic  original,  j~ai  Jj,  clearly  indicates  the  true  meaning. 


ABSOLUTE    SPACE  65 

you  understand  by  space  a  mere  relation  of  contiguity,  the 
whole  argument  becomes  meaningless.  But  the  reader  will 
realize  at  once  that  this  position,  while  apparently  attacking 
Zeno,  really  admits  his  argument,  i.  e.  that  space  as  an  all- 
encompassing  void  is  inconceivable  ;  there  is  only  a  relation 
of  contiguity.    There  is  place,  but  not  space. 

This  became  the  traditional  view  in  Jewish  philosophy. 
Gabirol  speaks  of  space  as  implying  '  the  immediacy  of  the 
surface  of  one  body  to  that  of  another  body',  or  simply 
\  the  contact  between  two  bodies  \77  Abraham  bar  Hiyya 
defines  space  as  '  that  which  envelopes  the  shape  of  a  body 
all  around  from  the  outside ' 78 — a  phraseology  which  is  not 
quite  fortunate,  but  whose  meaning  is  clear.  Joseph  Ibn 
Zaddik  maintains  that  *  the  true  meaning  of  space  is  pro- 
pinquity, for  there  is  no  container  without  something  con- 
tained, nor  anything  contained  without  a  container  ',79  and 
that  \  the  uppermost  sphere  needs  no  space  because  its  parts 
constitute  space  for  one  another  ',80  which  means  that  the 
largest  diurnal  sphere,  inasmuch  as  it  rotates  only  around 
its  axis,  and  does  not  as  a  whole  change  its  position,  does 
not  require  any  space  over  and  above ;  only  its  parts  change 
their  relative  position,  and  they  constitute  space  for  one 
another.     Abraham  Ibn  Daud  understands  by  space  '  that 

77  See  Fons  Vitae,  II,  14,  p.  74,  24  '  Locus  est  applicatio  superficiei 
corporis  ad  superficiem  corporis  alterius';  comp.  also  II,  14,  p.  49,  5 
'  Intentio  loci  noti  est  applicatio  duorum  corporum.'     Comp.  Mekor  Hayyim, 

11,21:  nriN  pju  ntstja  spa  not?  nipzn  n^rv  nipnn  nvn,  also  n,  23, 33. 

78  See  Hegyon  Hanefesh,   p.   3 :     D^X  J1K  HSin   131   Mil  DIpDil  *3 

prao  HW3D  bo  ipvt. 

79  Microcosm,  p.  15  :  QlpO  |W  *&  ftOD  WW  13\)jn  DlpDH  THICKS 
DlpD  &J  D01pn»  p«  DDlpnO  ^3D. 

so  ibid.,  P.  11:  nanb  Bipo  ubd  pbn  boo  tnpri?  ym  P«  P  hn« 

Cf.  FAjys.,  IV,  6. 

EF.  F 


66        PROBLEM    OF   SPACE    IN    JEWISH    PHILOSOPHY 

the  surfaces  of  which  compass  the  object  that  is  in  it'.81 
Aaron  of  Nicomedia,  the  Karaite,  writes :  '  The  primary- 
meaning  of  space  is  that  which  matter  occupies,  the  dimen- 
sions of  the  spatial  body  being  called  space.  It  also  denotes 
unoccupied  dimensions  or  the  whole  space.  And  thinkers 
are  at  issue  in  this  matter.  Some  apply  the  term  space  to 
that  which  is  in  contact  with  the  surface  of  the  body  and 
surrounds  it  on  all  sides,  others  apply  it  to  the  void  that 
embraces  the  universe ;  and  the  first  opinion  is  the  correct 
one.'82  Finally,  Gersonides  takes  the  same  standpoint 
when  he  argues  that  'above  and  below  relations  are  not 
due  to  any  mathematical  dimensions,  but  to  the  things  that 
bear  these  relations.  Thus  light  objects  move  upwards, 
heavy  ones  downwards  ;  and  when  there  was  nothing  light 
or  heavy  these  above  and  below  relations  did  not  exist  \83 

Thus  we  have  seen  how  the  Aristotelian  conception  of 
space  acquired  the  certainty  of  a  philosophical  tradition. 
Jewish  philosophers  used  it  as  a  self-evident  truism,  as  a 
logical  foundation  for  the  doctrine  of  creatio  ex  nihilo  and 
other  important  theological  doctrines,  and  it  occurred  to  no 
one  to  question  the  validity  of  this  foundation.  Then 
Hasdai  Crescas  appeared,  free  from  the  hypnotism  of  the 
Greek  master,  and  with  a  boldness  that  we  must  admire, 
considering  the  circumstances,  commenced  to  challenge 
Aristotelian  doctrines,  including  the  one  concerning  space, 
and  his  challenge  resounds  in  the  Dogmas  of  his  disciple 
Joseph  Albo,  and  even  in  the  works  of  Don  Isaac  Abrabanel 
by  no   means  an   independent   thinker.     Perhaps  it  was 

81  Etmmah  Ramah,  p.  16 :  tPEfQ  IDlpD  TIBC  DlpOn  NV1E>  TO  hi® 
vbv-  Perhaps  it  should  read  DH3in.  Comp.  the  quotation  from  Hegyon 
Hanefesh  in  note  78. 

82  Es  Hayyim,  ch.  ao.  83  Milhamot,  p.  371. 


ABSOLUTE  SPACE  67 

this  challenge  of  Aristotelianism  that  marked  the  beginning 
of  the  end  of  the  mediaeval  period  in  Jewish  philosophy.84 

Crescas  finds  four  difficulties  in  the  Aristotelian  notion 
of  space,  which  he  formulates  very  laconically,  as  '  the 
encompassing,  equal,  and  separate  surface  \85  These  '  diffi- 
culties '  are  not  very  difficult.  First  of  all,  he  argues,  the 
all-encompassing  sphere,  having  no  container  is,  according 
to  Aristotle,  in  no  space ;  but  all  things  have  their  existence 
in  space.  Consequently,  Aristotle  is  wrong.  Secondly, 
Aristotle  taught  that  every  element  has  a  certain  affinity 
towards  a  particular  place  at  which  it  is  at  rest  and  to 
which  it  is  in  motion.  Thus  air  is  naturally  at  rest  in  the 
concavity  of  the  celestial  layer  of  fire ;  everywhere  else  it 
can  be  at  rest  only  by  means  of  some  external  force.  Now 
if  this  be  true,  it  would  follow  that  either  the  inner  parts  of 
the  air  will  never  be  in  their  natural  place,  not  being  in 
contact  with  the  concave  surface  of  fire  to  which  they  strive 
as  parts  of  the  air  element,  or  else  their  natural  place  is 
different  from  that  of  the  whole — either  of  which  alternative 

84  The  reader  should  not  assume,  however,  that  Aristotelian  influences 
disappear  altogether  from  Jewish  thought.  Even  a  Kabbalist  like  Moses 
Botarel  speaks  of  Aristotle  in  laudatory  terms  and  accords  him  a  seat  in 
Paradise.  See  his  commentary  on  the  Book  of  Creation,  p.  26,  quoted  in 
Steinschneider's  Hebraische  Uebersetzungen,  p.  269.  But  the  name  of  the 
'  Philosopher '  no  longer  enjoyed  universal  and  unquestionable  authority. 
Thus  Isaac  Abrabanel,  though  often  accepting  Aristotelian  notions,  dares 
to  confer  upon  him  the  epithet  'Ancient  Serpent';  see  his  rivSIQD 
DVli>K,  II,  3. 

85  See  Or  Adonai,  ed.  Vienna,  i860,  p.  6,  where  the  definition  of  space 
is  formulated :  HiSl  XWT\  IfpOH  nDtJM  DIpDH  DVH.  Comp.  Narboni 
on  Guide,  I,  73,  prop.  2,  where  he  speaks  of  b*13jn  RHW1  Spp»n  rV^Snn. 
On  p.  15  Crescas  advances  four  arguments  against  this  Aristotelian  definition. 
Compare  also  Minhat  Kenaot,  by  R.  Jehiel  of  Pisa,  p.  26  :  (i.e.  of  space)  TVUS? 

)i  wun  DDipnoa  *ppon  Dtwn  rthan  Kin. 

F  3 


63  PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

is  absurd.  Thirdly,  how  do  the  celestial  bodies  move  in 
a  circle,  what  place  is  the  goal  of  their  striving  ?  Fourthly, 
Aristotle  held  that  a  rotating  ball  has  its  place,  though 
accidental,  in  the  axis  which  does  not  move ;  now  if  the 
axis  is  meant  to  be  a  material  part  of  the  ball,  it  is  evident 
that  motion  in  this  case  would  be  impossible  without  a  dis- 
integration of  its  parts,  and  if  it  is  meant  to  be  a  mere 
geometrical  line  that  can  be  drawn  through  the  centre,  it 
cannot  be  the  place  of  the  object. 

These  arguments  are  by  no  means  convincing.  Besides, 
they  are  not  altogether  relevant.  They  do  not  exactly 
'hit  the  mark'.  Crescas  is  more  aggressive  and  much 
more  convincing  in  the  concrete  problem  of  the  void,  which 
outgrows  from  this  whole  discussion,  and  which  I  reserved 
for  later  treatment.  I  shall  therefore  let  these  arguments 
pass  without  criticism.  It  should,  however,  be  remarked 
that  Albo  also  advances  four  arguments  against  the  Aris- 
totelian notion,  the  first  two  of  which  are  identical  with  the 
first  two  arguments  of  Crescas.86  Albo's  other  two  argu- 
ments are  as  follows  :  According  to  Aristotle,  the  place  of 
a  part  would  be  greater  than  the  place  of  the  whole,  for  a 
spherical  body  in  which  a  deep  break  has  been  made  will 
require  a  greater  surface  to  contain  it  inside  and  outside 
than  when  it  was  whole.  Thus  let  figure  i  represent  a  ball, 
and  let  figure  a  represent  the  same  ball  but  in  which 
a  deep  wedge-like  hole  has  been  hollowed  out,  and  let  the 
thread  in  both  cases  represent  the  Aristotelian  '  container ' 
or  place.  It  is  evident  that  figure  a  is  only  a  part  of 
figure  i,  and  yet  it  takes  a  greater  thread  to  embrace  the 
second  ball  than  the  first,  because  geometrically  A  OB  is 
greater  than  AB.  Consequently  a  part  would  occupy 
88  See  Dogmas,  II,  17.    See  also  D'man  1SD,  s.v. 


ABSOLUTE    SPACE 


69 


a  greater  place  than  the  whole,  which  is  absurd.  The 
second  argument  is  a  similar  one.  Take  a  body  which 
occupies  a  certain  amount  of  Aristotelian  space — or  let  us 
call  it  for  brevity's  sake,  place — and  divide  it ;  since  each 
segregated  part  now  requires  a  containing  surface  for  itself, 
the  total  amount  of  place  occupied  by  that  body  will  now 
be  greater.  The  further  you  divide,  the  greater  the  place 
that  it  will  occupy,  which  contradicts  the  Euclidean  law 


Fig.  i. 


Fig.  2. 


that  equal  bodies  occupy  equal  spaces.  These  two  argu- 
ments also  are  easily  met  by  the  idea  that  the  Euclidean 
law  of  space  cannot  be  applied  to  place. 

To  come  back  to  Crescas,  what  was  his  own  view  of 
space  ?  According  to  his  conception,  it  is  a  great  continuum, 
an  infinite  and  immovable  void,  ready  to  receive  material 
objects.  And  in  receiving  matter,  it  is  not  displaced,  for  it 
is  immovable,  but  on  the  contrary  it  embodies  itself  in 
it  and  becomes  concrete  extensity,  or,  as  Aristotle  called 
it,  the  interval  between  the  extremities  of  an   object.87 

87  See  Or  Adonai,  p.   15  b :    1PK  pflTl   KW   ~\Y\b  W8&1   Dip»nB> 

pay  pa  njnn  rrb  H30»"W  n^n  -raw  onpjym   vfpftn  nvion  pa 

.  .  »  Dil?.      See  also  17  b.    According  to  Simplicius,  Plato  denned  space  as- 


70  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

Aristotle  rejected  that  view  for  the  reason  that  all  bodies 
move  in  space,  and  if  the  interval  of  a  body  were  space 
in  itself,  we  would  have  space  moving  in  space.  To  this 
Crescas  answers,  there  are  no  various  spaces.  It  is  one 
infinite  and  immovable.  "When  matter  is  immersed  in  space 
it  is  like  a  net  in  a  stagnant  pool,  which  when  moving  does 
not  disturb  the  silent  waters.  In  other  words,  extensity 
and  void  are  not  two  kinds  of  space,  but  really  one ;  only 
the  former  has  had  an  admixture  of  matter  and  has  there- 
fore visualized  itself,  while  the  latter  is  pure  and  hence 
invisible.  Extended  matter  is  like  a  streak  of  sunlight  that 
has  become  visible  by  absorbing  particles  of  dust.  Thus 
we  have  no  phenomenon  of  space  moving  in  space.  Empirical 
space  and  absolute  space  are  one — this  is  the  great  idea  of 
Hasdai  Crescas. 

Crescas  found  a  faithful  follower  in  Joseph  Albo,  who 
incorporated  this  conception  of  space  in  his  Dogmas,  but 
Albo  seems  to  have  been  his  first  and  last  follower.  Con- 
ditions in  Spain,  for  some  four  centuries  an  asylum  of 
Jewish  culture,  were  no  longer  favourable  for  the  develop- 
ment of  free  thought.  The  end  of  the  fifteenth  century 
found  Spanish  Jewry  subjected  to  persecution  and  dire 
oppression,  which  strangled  the  zeal  for  genuine  speculation 
in  the  Jewish  breast  and  brought  the  progress  of  Jewish 
philosophy  to  such  an  abrupt  end.  It  is,  however,  to  the 
credit  of  the  Jew's  yearning  for  knowledge  that  even  in 
those  dreadful  times  a  man  like  Don  Isaac  Abrabanel,  one 
of  the  foremost  statesmen  of  Spain,  but  later  an  outcast 
of  the  land  which  he  faithfully  served,  found  moments  of 
leisure  in  the   intermissions  of  his  aimless  wandering  to 

to  StaoTTj/M  to  fieTagv  tuiv  iaxO'TOiv  rod  irtpiexovTos  (Simpl.,  Phys.,  IV,  p.  571). 
If  Simplicius  is  correct,  Crescas  takes  the  Platonic  standpoint. 


ABSOLUTE    SPACE  71 

compose  philosophical  treatises  which,  though  wanting  in 
originality,  display  a  vast  amount  of  erudition  and  ac- 
quaintance with  philosophical  systems.  In  the  question 
under  discussion  he  does  not  side  with  Crescas,  but  adopts 
the  Aristotelian  conception  of  space.88 

II.  The  preceding  discussion  as  to  whether  we  are  to 
understand  by  space  a  material  receptacle  or  an  unlimited 
continuum,  is  altogether  useless,  if  not  supplemented  with 
a  discussion  of  a  problem  which  is  implied  therein,  namely, 
the  existence  of  a  void.  The  Aristotelian  conception  in- 
volves a  cosmology  which  admits  of  no  void.  The  universe 
is  composed  of  spheres  one  within  the  other,  all  compact, 
with  no  space  between.  The  innermost  sphere,  sphere  A, 
has  its  place  in  the  concave  form  of  sphere  B,  and  sphere  B 
in  sphere  C,  and  so  forth.  The  uppermost  all-containing 
sphere  is  in  no  place :  it  is  the  limit  of  the  universe.  Thus 
there  is  place  ;  but  no  pure  space,  no  void,  whether  between 
things  or  outside  of  them.  On  the  other  hand,  if  we  mean 
by  space  an  unlimited  continuum  embodied  here  and  there 
in  a  concrete  material  object,  a  canvas  as  it  were  in  which 
some  fine  tapestry  is  woven,  we  naturally  postulate  the 
existence  of  an  unembodied  space  or  a  void.  Thus  so  long 
as  the  Jewish  thinkers  unquestioningly  accepted  the  Aristo- 
telian notion  of  space,  they  discarded  the  possibility  of  a 
void ;  it  was  Crescas  who  first  endeavoured  to  prove  that 
the  void  is  a  real  fact. 

It  is  noteworthy  that  the  existence  of  a  void  was  one  of 
the  great  issues  between  mediaeval  Aristotelianism  and 
Arabian  scholasticism  or  the  Kalam ;  the  former,  as  we 
have  seen,  vigorously  renouncing  it,  and  the  latter  vigorously 

88  txrhm  nfea,  iv,  3:  bn:  rra  ippon  nmn  nac  mh  new 


72  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

maintaining  it.  The  Mutakallimun  maintained  the  void, 
because  it  is  an  indispensable  element  in  any  system  which 
resolves  matter  into  segregated  particles  of  minute  magni- 
tude generating  all  phenomena  by  their  motion.89  Jewish 
thinkers,  we  have  found,  were  averse  to  atomism ;  so  that 
the  postulation  of  a  void  was  no  requisite  of  their  system. 
At  all  events,  Jewish  philosophy  before  Crescas  was  unani- 
mously against  the  existence  of  pure  space.90  Let  us  see 
some  of  its  chief  reasons. 

Joseph  ibn  Zaddik  offers  a  proof  from  nature.  Take 
a  pitcher  and  plunge  it  into  water  with  its  mouth  upside 
down.  No  water  will  come  in  the  pitcher.  Remove  the 
air,  and  the  water  will  instantly  rush  into  it,  so  as  not  to 
leave  a  vacuum.  Or  take  a  jar  with  a  perforated  bottom, 
fill  it  with  water;  of  course  the  water  will  issue  through 
the  bottom,  and  air  will  enter  through  the  top,  and  im- 
mediately fill  the  gap.  Now  fill  the  jar  with  water  again, 
and  close  it  so  tightly  as  to  leave  no  access  to  the  air; 
no  drop  of  water  will  leak  through  the  pores  of  the  bottom. 
This  clearly  shows  that  there  is  no  vacuum  in  nature.91 
The  argument,  by  the  way,  is  Aristotelian,  and  is  also  cited 
by  Narboni.92 

How  then  is  motion  possible  if  there  is  no  empty 
space?  In  a  compact  world  of  matter,  where  even  elbow- 
room  is  denied  us,  how  can  we  move  ?  Ibn  Zaddik  adopts 
the  Aristotelian  answer.     The  air  is  very  elastic,  being 

89  See  Guide,  I,  73,  prop.  a. 

90  Abraham  Ibn  Ezra  is  perhaps  an  exception  to  this  statement.  He 
nowhere  posits  the  void,  but  one  might  infer  it  from  the  atomistic  ideas  that 
he  expresses  in  the  fragments  called  flDtDPI  DTTB1  HCOnn  rUTty.  See 
above,  note  55. 

91  Microcosm,  p.  16. 

92  See  Narboni  on  Guide,  I,  73,  prop.  3. 


ABSOLUTE   SPACE  73 

easily  condensed  and  rarefied.  And  when  we  press  forward, 
we  set  up  a  system  of  condensation  before  us,  and  a  system 
of  rarefaction  behind  us.  Even  the  removal  of  a  drop  of 
water  thus  affects  the  whole  universe;  but  no  vacuum  is 
anywhere  formed.93  The  reader  will  realize  that,  as  Narboni 
rightly  remarked,94  the  atomists  could  not  have  taken  the 
same  view  in  explaining  atomic  motion  by  condensation 
and  rarefaction  without  being  compelled  to  assume  the 
existence  of  a  void,  because  the  atom  is  conceived  to  be 
an  indivisible,  non-magnitudinal  and  ultimate  reality,  and 
hence  can  neither  swell  nor  shrink. 

A  similar  argument  for  the  non-existence  of  the  vacuum 
is  adduced  by  Maimonides  from  the  science  of  hydraulics.95 
Water  is  being  carried  from  a  lower  to  a  higher  level  by 
means  of  a  pump  out  of  which  the  air  has  been  exhausted, 
the  underlying  principle  being  that  'nature  abhors  a 
vacuum ',  that  it  tends  to  fill  an  empty  space  as  soon  as 
it  is  formed. 

An  altogether  original  argument  was  suggested  by  the 
Kabbalist,  Isaac  Ibn  Latif.96  A  visual  sensation  of  light 
implies  a  certain  gas  medium  through  which  radiant  energy 
is  being  propagated  in  waves,  finally  impinging  the  retina 
of  our  eye,  thus  producing  a  sensation.  Ibn  Latif  was  of 
course  ignorant  of  the  modern  undulatory  theory  of  light ; 
instead,  he  believed  that  an  object  of  light  emits  certain 
material  corpuscles — similar  to  the  now  repudiated  New- 
tonian conception.  But  at  all  events  a  certain  medium  is 
required  through  which  the  radiant  energy  or  the  radiant 
corpuscles  are  transferred.  Hence  our  vision  of  the 
luminary  bodies  proves  the  total  absence  of  intervening 

93  Microcosm,  p.  16.  M  /.  c,  1,  73,  prop.  2. 

96  Ibid.,  prop.  3.  "  See  D^J?D  21,  section  60. 


74  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

vacuum.  It  is  curious,  however,  that  in  the  end  he  remarks 
as  follows :  ' .  . .  and  the  very  same  demonstration  for  the 
non-existence  of  the  void,  is  a  demonstration  for  its  existence ; 
and  understand  this,  for  it  is  sealed.'  How  this  argument 
also  proves  the  reality  of  a  void  is  not  easy  to  guess,  unless 
he  meant  that  the  radiant  waves  in  order  to  move  must 
have  free  space — a  contention  which,  as  we  have  seen,  has 
already  been  refuted  by  earlier  thinkers.  But  the  argument 
in  itself  is  noteworthy. 

The  reasons  so  far  advanced  are  drawn  from  the  realm 
of  nature,  and  all  they  may  prove  is  that  there  are  no  empty 
interstices  between  the  material  objects,  that  the  equilibrium 
of  the  world  demands  a  filling  up  of  all  gaps,  leaving 
nothing  empty.  They  demonstrate  the  familiar  maxim : 
'  Nature  abhors  a  vacuum  \  Of  course,  as  Solomon  Maimon, 
the  Kantian  interpreter  of  Maimonism,  correctly  suggested, 
nature  does  not  exactly  abhor  a  vacuum,  it  is  forced  to  fill 
it ;  that  is  to  say,  a  vacuum  is  a  natural  existence,  only  it  is 
obviated  by  external  forces.  When  the  air  is  exhausted 
from  the  tube,  the  water  is  forced  into  it  by  the  atmospheric 
pressure;  so  that  when  the  tube  is  too  high  for  the 
atmospheric  pressure  to  raise  the  water,  a  void  will 
naturally  form  in  the  tube.  This  physical  phenomenon 
was  entirely  overlooked  by  the  men  I  have  mentioned. 
The  mediaeval  term  horror  vacui  is  really  misleading.  At 
all  events,  those  arguments  tend  to  refute  the  existence 
of  void  within  the  material  realm,  or,  following  the  analogy 
of  our  previous  terminology,  empirical  void,  which  does  not 
mean  an  experience  of  a  void,  but  a  void  of  experience,  or 
a  blank  in  the  midst  of  objects  that  appeal  to  our  sensation. 
Now  what  of  absolute  void,  what  of  pure  infinite  dimen- 
sionality in  which  the  universe  is  supposed  to  exist,  is  it 


ABSOLUTE    SPACE  75 

real  or  fictitious  ?  Is  there  any  space  beyond  the  confines 
of  the  world?  Or  let  us  imagine  matter  annihilated  or 
non-existent,  would  there  be  space  after  all  ? 

Gersonides  answers  these  questions  negatively.  Tri- 
dimensionality  is  a  quality  of  matter;  take  away  matter 
and  you  have  no  space.  It  is  absurd  to  say  that  before 
the  creation  of  the  tangible  world  there  was  pure  space ;  for 
if  so,  why  did  God  create  the  world  in  this  part  of  the 
infinite  void  and  not  in  another  ?  The  void  is  alike  in  all 
its  parts,  no  one  of  which  owns  a  greater  possibility  of  being 
informed  and  embodied  than  another.  If  then  you  assume 
a  void,  you  have  to  assume  logically  a  coextensive  infinite 
matter,  which  is  likewise  absurd.  Hence  pre-existent  space 
is  an  impossibility.97  The  argument  is  based  on  the 
theory  of  creationism,  a  theory  no  longer  tenable  in  philo- 
sophical circles ;  but  the  whole  question  about  the  pre- 
existence  of  space  is  a  scholastic  one.  Gersonides,  however, 
goes  a  step  further,  and  endeavours  to  show  that  any  form 
of  empty  space  is  inconceivable.  There  is  a  patent  contra- 
diction involved  in  the  term  '  empty  space '.  Space,  we 
know,  is  measurable  and  infinitely  divisible.  But  empty 
space  means  that  there  is  nothing  existent,  in  short, 
nothingness,  and  how  can  we  conceive  of  nothingness  as 
measurable  or  divisible,  or  of  one  nothingness  as  greater 
than  another  ?  Consequently  empty  space  is  an  absurdum. 
The  argument  hides  a  certain  fallacy,  but  let  us  go  on  and 
see  the  concrete  example  which  he  offers  in  order  to 
demonstrate  the  absurdity  of  the  void.  Imagine  two  bodies 
separated  by  empty  space,  one  ABCD  and  the  other  F.FGH, 
placed  in  two  positions,  the  lines  AB  and  EF  in  one  position 
being  parallel  lines,  and  oblique  in  the  other. 

87  See  Milhamot,  p.  365. 


76  PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

Now  in  Figure  i  we  say  that  the  intervening  distance  or 
void  represented  by  AE  equals  BF;  while  in  Figure  1  we 
say  AE  is  greater  than  BF.  But  both  AE  and  BF  do  not 
represent  any  material  existence,  consequently  they  are 
zero,  and  how  can  zero  be  a  basis  of  comparison,  and  above 
all  how  can  one  zero  be  greater  than  another  ?  Hence  the 
void  is  an  absurdity.— Q.E.D.98  But  it  is  evident  that 
Gersonides  plays  hide-and-seek  with  the  notion  of  pure 
space.     This  term  stands  for  mere  dimensionality  devoid 


Fig.  i 


C  fc        F  <3 

Fig.  a. 

of  any  material  thing.  Now  if  one  were  to  count  things, 
he  would  of  course  have  to  leave  out  the  void,  and  consider 
it  mathematically  zero.  But  here  it  is  not  the  counting  of 
the  two  bodies  that  is  involved,  but  the  extension  of  the 
intervening  void ;  and  from  the  point  of  view  of  extension, 
the  void  is  a  definite  quantity  unless  it  has  been  previously 
demonstrated  that  the  void  is  an  impossibility — something 
that  is  here  to  be  proved.  Gersonides,  therefore,  in 
assuming  that  the  lines  of  extension  AE  and  BF  are  zero, 
is  clearly  arguing  in  a  circle. 

Gersonides,   however,   concludes  that  the  void   is   an 

98  Ibid.,  pp.  378  and  379. 


ABSOLUTE    SPACE  77 

illusion.  It  is  strange  that  such  an  acute  thinker  should 
fall  into  such  an  open  fallacy ;  perhaps  it  was  the  Aristote- 
lian system  to  which  he  mainly  clung  that  required  of  him 
such  a  conclusion,  and  the  need  of  a  conclusion  blinded  him 
to  the  validity  of  the  reasoning.  Reason  is  very  often 
sacrificed  in  order  to  suit  a  system.  At  any  rate,  Gersonides 
firmly  held  that  the  universe  is  finite;  that  there  is  no 
space  beyond  the  world.  But  here  a  logical  puzzle  pre- 
sented itself  to  his  mind.  '  There  is  no  space  beyond  the 
world ',  but  does  not  the  very  word  '  beyond '  suggest  space  ? 
Does  it  not  convey  the  notion  of  outstretched  plains,  even 
while  this  is  meant  to  be  denied.  Let  us  expand  that  brief 
statement ;  do  we  not  mean  that  there  is  no  space  in  the 
space  beyond  the  world  ?  Is  not  therefore  the  whole  idea 
about  the  finitude  of  space  meaningless  and  erroneous? 
Gersonides,  however,  does  not  despair.  The  puzzle  is  not 
real,  but  linguistic.  Human  language  fits  our  daily  needs, 
but  is  not  rich  enough  to  express  many  a  fine  shading  in 
reality.  It  is  incapable  to  express  the  absolute  absence  of 
space  in  terms  of  before  and  after,  just  as  it  is  incapable  to 
express  the  absolute  non-existence  of  time  in  the  relations 
of  before  and  after.  When  we  say,  what  was  before  the 
beginning  of  time  ?  we  experience  the  same  difficulty.  It  is 
not  however  real,  but  simply  verbal,  due  to  the  inadequacy 
of  language."  This  is  Gersonides's  solution  of  the  puzzle. 
Some  five  centuries  after,  Kant  also  grappled  with  this 
puzzle,  but  his  solution  was  different.  We  can  conceive  no 
end  to  space,  no  limits  beyond  which  there  is  no  space. 
Hence  space  must  be  a  necessity  of  thought,  a  form  of 
intention.  Which  solution  is  saner  this  is  not  the  place  to 
discuss. 

99  Ibid.,  p.  384. 


78  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

So  much  for  the  negative  side  of  this  void-discussion. 
This  side,  it  should  be  noted,  does  not  make  out  a  very- 
impressive  case.  Its  reasoning  is  sometimes  hackneyed, 
and  sometimes  faulty.  Judah  Halevi  counted  the  void  as 
one  of  the  things  that  common  sense  seems  to  accept,  and 
syllogistic  reasoning  rejects ;  10°  but  he  did  not  show  us 
what  this  'syllogistic  reasoning'  is.  Yet  although  the 
proposition  which  this  side  attempted  to  put  forth  had  no 
great  intrinsic  force,  it  had  that  force  which  is  in  every 
view  that  coincides  with  tradition.  It  traced  back  its 
lineage  to  Aristotle.  Ipse  dixit.  That  is  why  this  negative 
view  was  popular  in  Jewish  philosophy  for  so  long  a  time. 
At  last  the  affirmative  side  appears  on  the  scene,  represented 
by  one  man  only,  radical,  bold,  and  daring — Hasdai  Crescas. 
Let  us  hear  what  he  has  to  say. 

Crescas  does  not  enter  into  a  detailed  discussion  with  the 
followers  of  Aristotle,  he  attacks  straightway  Aristotle 
himself.  Incidentally  he  points  out  the  absurdity  of  Ger- 
sonides's  difficulty  with  empty  space  as  a  magnitude.  If 
you  remove  the  air  from  a  jar,  you  do  not  remove  extension 
along  with  it.  And  the  empty  extension  in  the  jar  is  of 
course  measurable  and  divisible.101  He  also  shows  in 
passing  that  finite  space  is  inconceivable,  because  what  is 
there  beyond?102  Crescas  evidently  rejects  Gersonides's 
explanation  by  an  appeal  to  linguistic  poverty.  He  also 
clears  another  difficulty  that  Gersonides  had  in  connexion 
with  the  void,  namely,  the  void  is  the  same  in  all  its  parts, 
why  then  did  God  create  the  finite  world  in  this  part  of  the 
infinite  void  rather  than  in  another  ?     Crescas  answers  that 

"°  Cosari,  in,  49 :  nipnn  Ttyn  maom  na^ncn   p*mn  "hmg 
nt  rroTiD  m^apn  meprn. 

ifll  See  Or  Adonai,  p.  15  a.  1<H  Ibid. 


ABSOLUTE    SPACE  79 

just  because  the  void  is  the  same  in  all  its  parts  it  is  absurd 
to  ask  why  God  should  have  created  the  world  in  another 
part  rather  than  in  this.103  His  main  charge,  however, 
Crescas  concentrates  on  Aristotle  himself.  He  examines 
his  arguments  singly  and  discloses  their  weakness.  We 
will  follow  the  order  of  his  treatment. 

1.  If  void  existed,  says  Aristotle,  there  would  be  no 
motion.  For  motion  is  either  natural  or  forced ;  natural 
motion  being  that  of  a  body  moving  to  the  place  to  which 
it  has  affinity,  as  an  apple  moving  downwards,  and  forced 
motion  being  that  of  a  body  moving  away  from  the  place 
of  its  affinity,  as  when  an  apple  moves  upwards.  But  a 
void  is  mitdammeh  hahalakim,  the  same  in  all  its  parts,  no 
one  of  which  can  enjoy  the  special  affinity  of  an  object. 
Hence  natural  motion  in  a  void  is  absurd.  And  since  it  is 
implied  in  forced  motion  the  latter  is  also  absurd.  More- 
over, imagine  an  arrow  hurled  from  a  bow-string;  now 
ordinarily  the  arrow  moves  on  by  virtue  of  the  fact  that 
the  air  which  has  also  received  a  violent  attack  from  the 
bow-string  becomes  a  propelling  power  for  the  arrow.  Now 
in  a  void  where  such  a  propelling  power  is  lacking,  we 
should  expect  that  no  matter  how  much  the  string  is 
strained,  the  arrow  should  powerlessly  fall  down,  as  soon 
as  it  leaves  the  string.  Thus  motion  in  any  of  its  forms 
is  impossible  in  a  void,  and  hence  the  void  cannot  be 
conceived  to  exist.  Thus,  instead  of  maintaining  that 
motion  is  impossible  without  empty  space,  the  true  idea 
is  that  motion  is  impossible  with  empty  space. 

To  this  Crescas  replies :  The  fault  of  this  argument  is 
chiefly  in  failing  to  realize  that  the  void  is  not  considered 
by  its  adherents  to  be  the  cause  of  motion,  but  only  the 

103  Ibid.,  p.  70  a. 


80  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

medium.  The  argument  seeks  to  disprove  the  idea  that 
the  void  is  cause — an  idea  maintained  by  no  one.  Aristotle 
argues  that  the  void  cannot  bear  any  special  attraction 
to  any  body,  and  since  that  attraction  is  the  basis  of 
motion,  the  latter  is  inconceivable  in  a  vacuum.  But  no 
one  claimed  that  it  does  have  any  peculiar  attraction. 
Gersonides  has  already  remarked  that  the  notions  of 
1  upward '  and  '  downward '  are  not  due  to  mere  mathe- 
matical dimensions,  but  to  the  objects  that  may  be  up  or 
down.  The  fire  does  not  seek  any  mathematical  dimensions 
above  it,  but  the  concave  lunar  surface.  Thus  it  is  not  the 
void  that  exercises  any  attraction  or  repulsion,  but  the 
bodies  in  it.  The  earth  attracts  the  apple,  and  there  may 
be  an  intervening  void,  yet  that  does  not  hinder  motion, 
but  on  the  contrary  helps  it,  serving  as  a  free  medium. 
Indeed,  the  whole  Aristotelian  position  is  questionable. 
A  medium  is  no  requisite  for  motion.  It  hinders  it ;  the 
rarer  the  medium,  the  freer  the  movement.  Light  objects 
move  upwards,  and  heavy  objects  move  downwards,  or 
rather — and  here  a  very  important  physical  theory  occurs 
to  his  mind — all  bodies  move  downwards,  only,  the  lighter 
bodies  are  pressed  upwards  by  heavier  downward  moving 
bodies.  And  all  this  goes  on  without  necessitating  a 
material  medium  which  is  really  an  obstacle  and  a  hindrance 
for  a  moving  body.  It  is  the  void  which  is  the  true  medium 
for  the  free  exercise  of  motion.104 

1.  The  second  and  third  arguments  of  Aristotle  are 
treated  by  Crescas  simultaneously.  Motion,  speaking 
mathematically,  is  a  function  of  two  variables :  the  medium 
and  the  motive  force.  Let  us  see  the  medium-variable 
first.  The  velocity  of  a  body  is  proportioned  to  the 
10*  Ibid.,  p.  i4aff. 


ABSOLUTE    SPACE  8l 

medium:  the  rarer  the  medium,  the  quicker  the  motion. 
If  we  could  imagine  a  medium  of  an  infinitely  rare  density, 
then,  all  other  things  being  equal,  the  body  would  move 
in  an  infinitesimal  time.  But  the  void  has  altogether  no 
density,  hence  a  body  will  move  therein  in  no  time  at  all. 
But  this  is  absurd,  for  the  distance  in  which  the  body 
moves  is  divisible,  it  is  a  succession  of  points ;  and  the 
moving  body  '  must  take  its  time ',  it  cannot  come  to 
the  second  point  before  it  passes  the  first,  and  when  it  is 
on  the  second  point,  it  is  not  yet  on  the  third.  Hence 
even  this  '  champion  racer '  must  take  cognizance  in  its 
movement  of  the  relations  of  before  and  after,  and  conse- 
quently must  take  up  some  time  after  all.  Therefore  the 
void  is  an  impossibility. 

The  impossibility  of  an  absolutely  timeless  movement 
is  further  corroborated  when  we  come  to  examine  the 
second  variable  of  motion,  i.e.  the  motive  force,  which 
forms  Aristotle's  third  argument.  The  velocity  of  a  body 
is,  all  other  things  being  equal,  directly  proportional  to  the 
propelling  power:  the  stronger  that  power,  the  swifter 
the  motion.  This  law  holds  true  in  the  hurling  of  a  weight 
upward  in  the  air,  as  well  as  downwards  in  the  water,  and 
we  should  expect  it  to  hold  good  also  in  the  case  of  a 
vacuum.  But  in  accordance  with  the  law  of  the  first 
variable,  a  body  moves  through  a  void  under  a  given  force 
in  no  time.  Now  double  that  force,  and  the  velocity  will 
have  to  be  doubled  too.  But  what  can  be  quicker  than 
timeless  motion  ?  Hence,  Aristotle  concludes,  the  void  is 
an  impossibility  and  an  absurdity.105 

To  these  two  arguments  Crescas  replies :  A  body  that 
is  impelled  to  move  by  a  certain  force  acquires  a  certain 

105  p.  5  a. 
EF.  G 


82        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

*  fundamental  velocity ' ;  that  is  to  say,  a  fundamental 
capacity  to  move  a  certain  distance  within  a  certain  time 
unimpeded  by  any  medium  like  water  or  gas.  When  that 
body  happens  to  meet  a  medium,  its  velocity  is  slackened 
of  course.  The  denser  the  medium,  the  slower  the  move- 
ment. Remove  the  medium,  and  the  body  will  resume 
its  initial  '  fundamental  velocity '.  Thus  the  law  that  the 
velocity  of  a  body  is  inversely  proportional  to  the  density 
of  the  medium  is  not  a  true  statement  of  fact.  Represent  it 
mathematically,  and  you  have 

v_  _  &      ,  _  nv 

Vf  ~  D  ;  D'  ' 

But  the  density  of  the  void  (Df)  equals  zero,  hence 
T»      DV 

V    =  =  oc   . 

o 

Thus  the  velocity  of  a  body  moving  in  a  vacuum  is  infinite, 
which  is  absurd,  as  Aristotle  himself  has  shown.  But  this 
whole  mathematical  formula  is  untenable.  The  true  law  is 
that  the  slackening  of  the  'fundamental  velocity  '  of  a  given 
body  is  directly  proportional  to  the  density  of  the  medium. 
Thus  representing  the  slackened  progress  by  6*,  we  have 

S'  =  D"  S'=^r;butZ>  =  o,    v  5  =  o. 

In  other  words,  a  body  moving  in  a  vacuum,  not  being 
impeded  by  any  medium,  will  move  according  to  its 
'  fundamental  velocity'.  It  is  just  as  unwise  to  argue  that 
inasmuch  as  a  body  moves  swifter  in  a  light  medium  than 
in  a  dense,  it  will  move  in  a  void  in  no  time  at  all,  as  it  is 
to  maintain  that  because  a  man  that  is  less  tired  will  move 
faster  than  a  man  that  is  more  tired,  a  man  that  is  not 


ABSOLUTE    SPACE  83 

tired  at  all  will  move  altogether  in  no  time.  Both  state- 
ments leave  out  of  consideration  the  principle  of  the 
fundamental  natural  velocity.106 

3.  The  fourth  argument  of  Aristotle  is  as  follows :  The 
void  is  conceived  as  mere  tridimensionality,  ready  to  receive 
material  objects,  the  dimensions  of  the  thing  uniting  with 
the  dimensions  of  the  void,  and  forming  one.  But  how  is  it 
possible  ?  How  can  two  ells  form  one  ell  ?  And  if  it  is 
possible  in  the  case  of  matter  and  void,  why  should  it  be 
impossible  in  the  case  of  matter  and  matter  ?  We  will  thus 
have  to  suspend  the  law  of  impenetrability,  for  the  reason 
why  two  bodies  cannot  occupy  the  same  space  at  the  same 
time,  is  not  because  they  are  black  or  warm  or  in  any 
other  way  qualified,  but  because  they  have  dimensions. 
And  yet  some  assume  that  a  body  can  penetrate  a  void 
which  is  spatiality  itself.  If  then  this  were  true,  there 
should  be  an  equal  possibility  of  compressing  two  or  more 
material  bodies  into  one,  and  we  should  thus  be  enabled  to 
compress  the  whole  universe  into  a  tiny  insignificant  speck. 
Thus  the  assumption  of  the  void  leads  us  into  monstrous 
absurdities.107 

To  this  Crescas  replied  :  Two  things  cannot  occupy  the 
same  space  in  the  same  time,  not  because  each  one  of  them 
has  its  own  dimensions,  but  because  each  one  has  dimen- 
sional matter.  In  other  words,  in  order  that  a  body  should 
be  impenetrable  it  must  have  two  things  combined :  spa- 
tiality and  corporeality.  And  just  as  unextended  matter, 
if  such  a  thing  were  conceivable,  would  not  be  impenetrable, 
so  spatiality  devoid  of  matter  could  not  resist  the  intrusion 
of  a  material  body.  That  is  why  an  ell  of  matter  and  an 
ell  of  a  void  can  so  combine  as  to  form  one.      Crescas 

106  Ibid.,  p.  14  b.  «"  Ibid.,  p.  5  a. 


84    PROBLEM  OF  SPACE  IN  JEWISH  PHILOSOPHY 

herewith  also  replies  to  Zeno's  argument  that  if  space  were 
real,  it  would  be  in  space ;  for  all  things  real  are  in  space, 
and  so  on  ad  infinitum.  It  is  only  material  spatiality  that 
occupies  and  monopolizes  a  certain  space  so  as  not  to  admit 
any  other  body  to  immigrate  into  its  domain ;  pure  spa- 
tiality has  no  policy  to  refuse  immigration,  on  the  contrary, 
it  bids  welcome  to  any  object  that  seeks  to  settle  within  its 
borders.  Hence  the  void  does  not  strictly  speaking  '  occupy ' 
space,  and  is  always  ready  to  be  intruded  as  long  as  it  has 
not  been  invested  with  corporeality.108 

Such  were  the  refutations  that  Crescas  hurled  against 
the  Aristotelian  position.  The  reader  will  undoubtedly  be 
impressed  by  the  soundness  of  the  argument,  as  well  as  by 
his  turning  his  back  on  Aristotelian  physical  notions,  and 
catching  glimpses  of  the  modern  science  of  physics.  We 
may  nowadays  repudiate  the  possibility  of  an  absolute  void 
and  claim  that  there  is  an  all-filling  and  all-penetrating 
ether,  but  the  existence  of  ether  is  after  all  only  a  hypo- 
thesis. Empirically  the  void  is  by  no  means  denied.  It 
should  also  be  noted  that  while  the  Mutakallimun  postu- 
lated the  existence  of  a  void  merely  to  suit  their  atomic 
system,  Crescas  who  did  not  adopt  the  atomic  standpoint 
takes  a  different  course.  He  first  disproves  the  seemingly 
convincing  Aristotelian  arguments,  and  having  removed  by 
sound  reasoning  the  traditional  prejudice,  he  shows  that 
the  void  is  attested  by  our  daily  experience.  That  is  why 
his  theory  of  the  void,  and  not  that  of  the  Arabian  theolo- 
gians, forms  a  real  contribution  to  the  history  of  philosophy. 
Sometimes  negative,  destructive  reasoning  is  more  important 
than  positive  reasoning.  To  destroy  the  enemy  is  to  win 
the  battle.     We  should  also  mention  in  this  connexion 

108  Ibid.,  p.  14  b. 


ABSOLUTE    SPACE  85 

Crescas's  discarding  the  Aristotelian  notion  that  different 
elements  strive  for  different  places,  that  fire  and  air  naturally 
tend  upwards.  Crescas  reduced  this  variety  of  forces  to 
one  force  of  gravitation.  All  bodies  are  attracted  down- 
wards, only  air  being  light  is  pressed  upward  by  some  heavier 
matter.  '  Light '  and  '  heavy '  are  not  different  in  quality, 
as  Aristotle  meant,  but  different  in  degree,  the  degree  of 
attraction  that  the  earth  exercises  from  them.109  This  uni- 
fication and  centralization  of  forces  rids  us  altogether  of 
the  Aristotelian  illusion  of  different  '  affinities '  and  '  natural 
places',  notions  which  play  a  considerable  part  in  the 
problem  of  place  versus  space.  Thus  these  two  theories 
of  Crescas,  the  defence  of  the  void  and  the  unification  of 
forces,  are  landmarks  in  the  progress  of  Jewish  thought. 

Coming  to  Isaac  Abrabanel,  we  are  not  a  little  dis- 
appointed. Instead  of  continuing  with  the  development  of 
the  pure  space  problem  along  the  lines  of  Crescas,  he  goes 
back  to  Aristotelianism.  This  does  not  mean  that  he  did 
not  read  the  Light  of  God.  He  not  only  read  it,  but  was 
even  so  much  infatuated  with  some  parts  of  it  that  he 
incorporated  them  into  his  works  and  forgot  to  label  their 
real  authorship.  Compare  for  example  Light  of  God,  p.  70, 
and  Abrabanel's  Works  of  God,  IV,  3.  But  the  plagiarist 
is  not  always  the  disciple.  He  thus  returns  to  the  old-time 
definition  of  space  as  '  the  surrounding  equal  and  separate 
surface'.110  He  adopts  the  view  of  Averroes  that  space 
came  into  being  with  the  creation  of  the  material  world,111 
that  is  to  say,  that  there  was  no  pre-existent  empty  space. 
He  thus  answers  the  question  why  God  created  matter  ia 

109  Ibid.,  p.  9  a. 

110  DM^X  ni^ySD,  IV,  3.     See  above,  note  87.. 
»"  Ibid.,  II,  1. 


86         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

this  part  of  the  void  rather  than  another, — there  was  no 
pre-existent  void  altogether ;  and  he  cites  a  similar  view  of 
St.  Thomas,  '  sage  of  the  sages  of  the  Gentiles  \112  The 
reader  will  readily  see  the  eclectic  nature  of  his  standpoint. 
Yet  there  is  one  passage  in  his  work  which  deserves  being 
quoted  at  length,  serving  as  a  fit  conclusion  to  this  chapter. 
It  deals  with  the  problem  why  the  mind  cannot  think  of 
finite  space,  of  limits  to  extensity,  why  even  in  our  speaking 
of  an  end  to  the  dimensionality  of  the  universe,  we  seem  to 
imply  a  '  beyond '.  We  have  seen  that  Gersonides  held  this 
difficulty  to  be  purely  linguistic.  Crescas  on  the  other 
hand  cited  this  as  a  proof  for  the  infinity  of  space,  just  as 
Kant  inferred  from  it  that  space  is  a  necessity  of  thought. 
Abrabanel  takes  a  view  similar  to  that  of  Gersonides,  but 
there  is  a  strong  note  of  modernity  in  his  explanation. 
'  It  is  impossible ',  he  says,  '  to  conceive  the  beginning  of 
time  without  a  pre-existent  time.  Also  the  limitation  of 
the  material  world  is  inconceivable  without  a  beyond- 
existing  place.  But  this  difficulty  of  conceiving  temporal 
or  spatial  finitude  is  purely  mental,  and  does  not  disprove 
real  finitude.  It  is  in  like  manner  hard  to  conceive  of  a 
thing  coming  into  actual  existence  without  thinking  of 
a  preceding  potentiality  ;  yet  of  course  it  does  not  mean 
that  there  was  actually  a  pre-existent  potentiality,  but  only 
an  intellectual  idea  of  such  a  potentiality.  All  this  is 
a  result  of  the  fact  that  the  phenomena  perceived  by  our 
senses  always  have  things  beyond  them  in  space  and  things 
before  them  in  time,  and  that  before  these  phenomena  are 
actual  they  are  potential ;  so  that  these  relations  of"  before" 
and  "  beyond  ",  always  present  in  our  perception  of  things, 
have  impressed  themselves  on  our  minds  so  deeply  as  to 
"2  Ibid.,  VI,  3. 


ABSOLUTE  SPACE  87 

be  unable  to  conceive  of  things  without  those  relations. 
But  after  a  certain  amount  of  reflexion  the  mind  can  correct 
this  error  arising  from  perception,  and  can  rid  itself  of  its 
acquired  habit,  and  come  to  realize  that  reality  is  not 
absolutely  conditioned  by  those  relations.' 113 

This  is  how  Abrabanel  seeks  to  explain  why  space  is 
seemingly  a  necessity  of  thought,  so  that  the  mind  is  unable 
to  conceive  bounds  to  the  space  of  the  universe.  It  arises 
from  a  '  habit '  which  the  human  mind  contracted  from  its 
perceptual  experience  to  seek  a  beyond  for  all  things.  Yet 
it  takes  only  a  certain  amount  of  mental  energy  by  way  of 
reflexion  to  transcend  this  genetically  acquired  habit,  and 
conceive  of  an  absolute  finitude  of  space.  It  is  not  a  necessity 
of  thought,  but  a  habit  of  thought ;  and  it  is  the  business  of 
a  philosophical  mind  to  shake  it  off. 

But  this  leads  us  directly  to  our  next  problem  concerning 
the  infinity  of  space ;  and  as  the  contents  of  this  chapter  do 
not  require  any  recapitulation,  we  will  pass  on. 

113  Ibid.,  IV,  3. 


CHAPTER   III 
Infinite  Space 

One  of  the  problems  that  have  troubled  the  human 
mind  is  the  problem  of  space ;  and  one  of  the  aspects  of 
space  that  have  troubled  the  human  mind  most,  is  its 
infinity.  From  the  philosopher  of  Stagira  to  the  philosopher 
of  Konigsberg,  the  subject  of  the  infinity  of  space  did  not 
cease  to  defy  and  baffle  human  ingenuity.  Our  present- 
day  thinkers  are  mostly  silent  on  this  topic.  They  dread 
the  contest,  but  they  have  not  overcome  it.  It  still  lies 
like  an  invincible  brute  ready  to  enter  the  arena.  Such 
being  the  case,  it  would  be  simply  preposterous  to  claim 
that  Jewish  philosophy  may  boast  of  having  solved 
altogether  this  overwhelming  difficulty,  but  I  do  claim 
that  in  the  course  of  the  progress  of  Jewish  thought  some 
suggestions  were  made  that  might  lead  to  a  new  and  better 
understanding  of  the  problem  ;  and  to  understand  it  would 
be  half  way  to  its  complete  solution. 

Let  us  first  turn  to  Aristotle,  who  may  always  serve  as 
a  text  in  any  discourse  on  mediaeval  philosophy.  His  ideas 
about  infinity  which  are  found  in  the  third  book  of  the 
Physics,  and  in  the  tenth  of  the  Metaphysics,  are  briefly 
thus.  On  the  one  hand  we  find  that  infinity  is  undeniable. 
88 


INFINITE    SPACE  89 

Time  is  unbegotten  and  indestructible.  We  cannot  conceive 
of  a  moment  of  time,  a  Now  which  is  an  absolute  beginning 
of  a  series  of  duration.  Every  Now  looks  on  one  side  to 
a  past  and  on  the  other  to  a  future :  it  has  a  before  and 
after.114  On  the  surface  it  may  seem  strange  that  a  similar 
argument  could  not  be  advanced  to  prove  the  infinity 
of  space :  every  Here  is  on  one  side  in  touch  with  a  before, 
and  on  the  other  with  a  beyond.  But  the  argument  is 
really  a  deeper  one.  It  is  repugnant  to  the  entire  Aristo- 
telian standpoint  of  causation,  the  denial  of  miraculous 
creationism,  to  assume  a  Now  which  was  not  caused  by 
a  previous  one.  Time  which  marks  the  duration  of  the 
beginningless  and  endless  development  of  things  must  in 
itself  be  infinite.  On  the  other  hand,  there  must  be  a  limit 
to  material  existence.  Matter  is  limited  by  superficies,  and 
hence  finite  ;  and  to  speak  of  an  infinite  number  of  material 
bodies  is  also  absurd,  for  a  number  is  that  which  can  be 
counted,  and  hence  likewise  finite.  Besides,  an  infinite 
body  would  be  either  simple  or  composite.  It  could  not  be, 
however,  a  simple  body,  similar  to  the  one  assumed  by  the 
earlier  physicists,  for  then  it  would  have  consumed  by  its 
infinite  power  all  other  finite  elements,  and  would  have 
created  all  things  single-handed ;  but  such  a  monistic  theory 
is  contradicted  by  the  fundamental  phenomenon  of  change 
which  implies  the  existence  of  contraries  in  the  universe. 
Nor  could  that  infinite  body  be  a  composite  without  being 
either  a  finite  number  of  infinites  or  an  infinite  number  of 
finitudes,  either  alternatives  being  impossible.  Thus  after 
a  series  of  arguments  Aristotle  concludes  the  finitude  of 
spatial  existence.  How  then  is  it — the  question  is — that 
infinity  seems  to  be  real  in  time  but  unreal  in  space  ? 
114  Comp.  Or  Adonai,  p.  62  a  ;   also  DTl^K  n^JJBC,  V,  3. 


90        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

An  explanation  for  this  antinomy  Aristotle  finds  in  the 
nature  of  the  concept.  It  is  in  accord  with  his  general 
dynamic  standpoint.  Infinity  denotes  duration  rather  than 
simultaneity,  succession  rather  than  co-extension.  Infinity 
never  is,  but  is  perpetually  becoming.  Hence  time  can  be 
represented  as  endless,  for  it  is  a  succession  of  fleeting 
moments,  each  one  vanishing  and  making  room  for  another. 
But  when  you  seek  to  attain  the  infinite  by  means  of  a 
synthesis  of  spatial  parts,  you  are  aiming  not  at  an  endless 
process  of  becoming,  but  at  an  endless  state  of  being  which 
is  not  postulated  by  the  true  notion  of  the  infinite.  The 
unlimited  is  not  actual  but  potential,  meaning  by  the  latter 
term  not  the  potentiality  of  the  brass  that  can  become 
an  accomplished  fact  in  the  form  of  the  statue,  but  a 
peculiar  potentiality  like  that  of  time,  which  though  actual 
only  in  an  insignificant  and  vanishing  moment,  constantly 
unfolds  itself  in  a  never-ending  succession  of  decay  and 
regeneration.'  It  is  a  process,  not  a  state.  The  usual 
meaning  of  the  infinite,  says  Aristotle,  is  that  beyond 
which  there  is  nothing,  but  the  true  meaning  is  that  which 
always  has  something  beyond. 

This  analysis  of  infinity  is  extremely  suggestive.  It 
might  be  shown  what  a  host  of  perplexing  difficulties  would 
vanish  in  this  new  light,  as  we  shall  see  in  the  sequel.  But 
it  is  unfortunate  that  Aristotle  himself  did  not  fully  realize 
the  immense  fruitfulness  of  its  suggestiveness.  He  seem- 
ingly forgets  very  soon  this  well-defined  position,  namely, 
that  things  are  always  and  everywhere  finite,  but  reveal 
the  infinite  in  the  process  of  change  and  duration,  just 
as  in  the  arithmetical  convergent  series  every  term  is 
limited  and  gives  us  a  limited  quantity  when  added  up 
with    the   preceding   terms,   but   there   is    the   infinity  of 


INFINITE    SPACE  91 

progression,  a  possibility  of  enlarging  the  number  of  one 
unit  to  all  eternities.  For  with  this  distinction  between 
state  and  process  clearly  in  his  consciousness,  how  could 
he  possibly  speak  of  a  realizable  infinitesimal  by  means  of 
division  ?  My  impression  is  that  Aristotle  fell  a  victim 
to  his  terminology,  to  his  use  of  '  potentiality ',  which  always 
implies  something  actual,  to  express  his  notion  of  infinity, — 
an  expression  which,  as  he  himself  felt,  hardly  suits  the 
meaning.  The  whole  distinction  between  infinite  divisibility 
and  infinite  augmentation,  the  former  being  affirmed  and 
the  latter  denied,  is  unintelligible  :  practically  no  one  would 
believe  that  we  may  divide  an  object  ad  infinitum,  and 
theoretically \  even  the  celestial  firmament  can  form  no 
limit  to  our  augmentation.  In  the  history  of  the  Jewish 
conception  of  infinity,  this  latter  potential  notion  was  at 
first  dominating  until  the  former  progressive  notion  was 
taken  up  and  modified  by  Gersonides.  Let  us  follow 
closely  this  meandering  path  of  the  idea  of  infinity  through 
Jewish  philosophy. 

Beginning  with  Saadya.  we  find  that  the  material 
universe  is  held  to  be  limited,  having  a  terrestrial  centre 
and  a  celestial  circumference.115  This  finitude  of  matter 
means  also  the  finitude  of  space,  for,  as  we  have  seen,  the 
void  was  not  posited  by  the  earlier  Jewish  thinkers.  Saadya 
pays  more  attention  to  the  theory  of  temporal  infinity 
maintained  by  Aristotle,  the  refutation  of  which  theory, 
though  somewhat  beyond  the  pale  of  this  work,  is  never- 
theless relevant  because  of  its  application  to  spatial  infinity. 
It  is  ridiculous,  he  holds,  to  say  that  time  had  no  beginning, 
for  then  an  infinite  number  of  points  have  already  elapsed  ; 
115  Emunot,  I,  p.  56  :   JV^l"!  tik  VV  ^ISiVtff  JV3  pRTti  DIMWIT 

DiTnu*aD  w&ffh  attoi  jjwMG  pNn  nvm. 


92        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

in  other  words,  this  present  moment  would  be  the  final 
term  of  an  infinite  series,  but  an  infinite  series  is  that  which 
cannot  be  completed.116  Moreover,  every  passing  day  is 
added  to  the  past,  and  detracted  from  the  future,  but 
anything  that  has  room  for  an  increment,  that  can  be 
turned  into  a  greater  magnitude,  is  by  no  means  infinite.117 
Furthermore,  time  is  the  measure  of  the  spherical  move- 
ments ;  and  if  the  former  is  conceived  to  be  beginningless, 
the  latter  must  also  have  a  claim  to  eternity.  But  those 
spherical  movements  are  not  uniform,  there  is  a  variety 
of  ratios  between  them,  while  one  sphere  makes  one  revolu- 
tion, another  sphere  ma)>-  make  three  hundred  and  fifty- 
five  revolutions.  If  the  eternity  hypothesis  is  correct,  both 
spheres  have  made  an  infinite  number  of  revolutions,  yet 
sphere  B  must  have  certainly  made  $$$  times  as  many 
revolutions  as  those  of  sphere  A.  Consequently  one  infinity 
would  be  greater  than  another  infinity,  which  is  absurd, 
because  the  infinite  is  greater  than  the  greatest  conceivable 
quantity.118  Hence  temporal  infinity  is  an  impossibility. 
These  arguments,  it  should  be  noted,  are  mentioned  by 
Halevi 119  among  the  proofs  of  the  Mutakallimun  for  the 
theory  of  creation. 

«« ibid.,  i,  59 :  may  mnn  »a  TiyT  nwm  nwy  vureo  -ipmi  . . . 
n^inn  nrvn  xb  ivban  pi  "b  w  ^bibi  ^n  ny*anp  ny  pin  by 

n2  D12iy-  See  Guttmann's  Die  Religionsphilosophie  des  Saadia,  p.  40, 
note  3. 

"7  ibid,  Part  I,  P.  74 :  naDin  ton  b:b:b  pirn  eibin  dv  bat?  wm 
w  jnonm  namnn  baiD  Nine?  not  Tnyn  p  jnom  *ibnsj>  no  bv 
wwn  naTio  ivbaro  irob  rvban. 

118  /«rf. :  &*3-iya  Dnxpp  *iy  nisbnno  own  rojnan  i»n  netoi 
nro  nnv  byi  B>cm  onpem  niND  cbtr  byi  bca  D^bs?  by  nvp  by 
rvban  ib  b*  one  nnx  ba^  wjrr. 

119  See  Cosari,  Part  V,  ch.  i8;  First  Axiom. 


INFINITE    SPACE  93 

Bahya  has  the  following  to  say  about  the  infinite.  He 
admits  that  number  is  infinite.  There  seems  to  be  no  end 
to  the  possibility  of  counting,120  but  actually  everything  is 
finite.  Imagine  a  line  AB  drawn  out  ad  infinitum,  and 
take  off  a  definite  part  A  C 

A         C B__ 

Now  BC  cannot  be  finite,  for  two  finite  lines  make  no 
infinite.  But  AB  is  of  course  greater  than  CB.  Thus  one 
infinite  would  exceed  another  infinite,  which  is  absurd. 
Moreover,  the  very  possibility  of  a  part  implies  that  the 
whole  line  must  be  finite,  for  a  part  bears  a  definite  ratio  to 
the  whole,  and  is  the  unit  of  measurement.  Indeed,  the 
extensity  of  an  object  is  that  property  of  it  by  virtue  of 
which  it  can  be  measured  by  a  part.  But  the  part  can  bear 
no  ratio  to  the  infinite.  Consequently  there  can  be  no 
infinite  extensity.121 

After  Bahya,  a  full  century  elapses,  marking  a  blank  in 
the  history  of  the  infinite,  except  perhaps  for  Gabirol's 
remarks  that  infinite,  spatial  or  temporal,  is  due  to  form- 
lessness, for  that  which  has  form  must  also  be  well  defined 
in  its  limits — a  purely  Aristotelian  position  identifying  the 
infinite  with  the  indefinite.122    At  last  we  come  to  Abraham 

120  see  nmbn  main  nwwi  w ;  <*.  8 -.  \wb  nbsn  pa  j  also  ch.  5 : 
invp  wo  6*"tt3i  iwsa  m5>an  b  pwp  nan  unavroa  r&w  dni 
P«d  ns^n  nw  dki  pqd  £ab  amp  rww  raws  nma  newi  mra 
no  wm  n^an  £  jw  nana  hna  n^an  n?  jw  nan  nw  n^an 

N"K£>.  This  argument  is  mentioned  in  Spinoza's  Ethics.  See  his  note  to 
Part  I,  prop.  xv. 

"!  ibid.,  ch.  5 :  bn  |*«  *a  fa  &  ^  pbn  \b  &p  no  fa  <a  yiTn  jd 
rpfan  ^  psp  no!?  pbn  nvni>  |3rv  xbi  vpbn  !>fa  tfb, 

12a  Fons  Vitae,  IV,  6,  p.  224  •  Res  autem  non  est  finita  nisi  per  suam 
formam  quia  res  quae  infinita  est  non  habet  formam  qua  fiat  unum  et  differat 
ab  alia  ;  et  ideo  essentia  aeterna  est  infinita  quae  non  habet  formam.'  Comp. 
V,  23,  p.  300,  and  29,  p.  309. 


94        PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

Ibn  Daud,  who  reiterates  the  Aristotelian  position  that 
only  number,  which  has  a  potential  existence,  is  infinite, 
but  all  actual  things  are  finite.  This  thesis  rests  on  the 
following  four  arguments,  all  except  the  first  one  being 
Aristotelian. 

i.  Let  two  lines  AB  and  CD  be  drawn  ad  infinitum. 

A  B 


On  CD  mark  off  a  finite  segment  CE.  Let  the  line  ED  be 
superposed  on  AB  so  that  point  E  coincides  with  point  A. 
Now  the  question  is,  is  ED  equal  to  AB?  It  ED  equals 
AB,  it  will  also  equal  CD,  but  how  can  a  part  be  equal  to 
the  whole  ?  If  ED  is  less  than  AB,  how  can  one  infinity- 
be  smaller  than  another  ?  And  if  ED  is  not  infinite,  how 
does  ED  plus  CE,  two  finite  lines,  make  an  infinite  line  ? 
This  argument  resembles  Bahya's  argument  with  one  line. 

2.  There  can  be  no  infinite  number  of  things,  for  a 
number  is  that  which  has  been  counted  over,  but  infinity  is 
that  which  cannot  be  counted  over.  Consequently  an 
infinite  number  is  a  contradiction.  Besides,  a  series  has  at 
least  one  limit,  but  in  a  beginningless  and  endless  series  all 
terms  are  intermediary.  Consequently  an  absolutely 
infinite  series  is  inconceivable. 

3.  An  infinite  body  would  not  be  in  place,  for  that 
implies  a  containing  body,  and  hence  a  larger  magnitude 
than  itself.  But  what  is  larger  than  the  infinite?  Here 
the  reader  may  object  that  from  the  Aristotelian  standpoint 
not  all  things  are  in  space.  The  all-containing  sphere  is 
itself  not  contained. 

4.  An  infinite  body  would  not  be  at  rest,  for  a  body  is 


INFINITE    SPACE  95 

only  at  rest  in  its  '  natural  place ',  which  an  infinite  body 
does  not  have.  Nor  would  it  be  in  motion,  for  a  moving 
body  leaves  one  place  and  occupies  another  place  which  it 
has  not  before  occupied.  But  no  place  is  free  from  the 
infinite.     Hence  an  unlimited  body  is  impossible.123 

A  critical  survey  of  these  four  arguments  brings  out 
a  very  important  point.  We  find  that  the  fourth  argument 
is  based  on  an  absurd  fiction  of  'natural  places'.  The 
objection  to  the  third  has  been  given.  It  is  the  second 
argument  that  is  truly  valid,  and  defeats  the  first  argument. 
It  points  out  the  absurdity  of  believing  in  a  numerical  or 
spatial  quantity  that  is  infinite.  If  quantity  means  any- 
thing at  all,  it  is  a  well-defined  relationship  between  the 
whole  and  a  supposed  part.  The  only  difference  between 
numerical  and  spatial  quantity  is  that  the  one  denotes 
a  discrete  nature  and  the  other  a  continuous  one.  But 
whether  it  is  ten  discrete  units  or  ten  continuous  inches,  the 
relationship  between  the  whole  and  the  part  is  limited, 
nothing  more  and  nothing  less.  Infinity,  however,  is  that 
which  has  no  limit,  and  hence  cannot  enter  such  relationship 
at  all.  Therefore  an  infinite  quantity  means  nothing  else 
than  an  infinite  finitude,  which  is  utterly  meaningless.  But 
if  this  is  true,  the  fallacy  of  the  first  argument  of  Ibn  Daud, 
and  with  it  many  more  arguments  that  may  possibly  be 
fashioned  after  this  model,  becomes  quite  evident.  If 
infinity  has  no  quantitative  relationships,  of  course  nothing 
can  be  added  to  it  or  detracted  from  it — which  means 
a  change  in  those  relationships;  and  the  non-existence 
of  infinity  cannot  be  proved  on  that  account.  This 
point  was  noticed  by  Maimonides,  and  amplified  by 
Moses  Narboni. 

12s  Emnnali  Ramah,  pp.  15  ff. 


96        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

In  his  exposition  of  the  Kalam  m  Maimonides  refers  to 
some  of  the  arguments  adduced  by  that  school  against  the 
infinite.  Now  Maimonides  himself  as  an  adherent  of  the 
Ptolemaic  system  of  astronomy,  and  the  creationistic  theory, 
and  as  an  opponent  of  the  belief  in  a  void,  of  course  maintains 
absolute  finitude  in  space  as  well  as  in  time.  Only  he  finds 
fault  with  the  particular  arguments  on  the  basis  of  which 
the  Mutakallimun  negate  infinity.  They  argue  that  if  the 
world  had  no  beginning  in  time,  there  would  have  elapsed 
up  to  this  moment  an  infinite  number  of  points  and  an 
infinite  number  of  spherical  revolutions  and  an  infinite 
number  of  transient  accidents.  This  whole  process  of 
fleeting  moments  and  revolving  spheres  and  transitory 
accidents  still  goes  on,  and  a  thousand  years  from  to-day 
these  infinites  will  be  swelled  by  a  certain  number,  and  the 
infinity  then  will  be  greater  than  an  infinite  to-day.125 
Furthermore,  if  the  eternity  of  the  world  is  true,  every 
celestial  body  has  had  an  infinite  number  of  revolutions. 
Now  there  is  a  definite  ratio  between  these  revolutions. 
While  the  terrestrial  globe  completes  its  circuit  once  a  year, 
the  lunar  globe  completes  its  circuit  twelve  times  in  a  year. 
It  makes  no  difference  how  long  you  allow  these  two  spheres 
to  revolve,  the  ratio  will  always  remain  12  : 1.  Now  allow 
them  to  revolve  ad  infinitum,  the  numbers  of  their  revolu- 
tions will  be  infinite  ;  but  one  infinity  will  be  twelve  times 

12^  Guide,  I,  74,  seventh  argument ;  comp.  Cosari,  V,  ch.  18,  First 
Axiom. 

125  See  also  Es  Hayyim,  ch.  X:   ivbri   pKP  "m   NtfO*   p   t6  DNt? 

nr  Nnn  dw  tj^xa  nmb  nonai?  "iwa  )b  rrbn  jw  hdd  nnT1  )b 

1BDW  iriKn  12^1  HT  -IID  "ins.     See  also  Milhamot,  p.  343:  I^SN  "WC 

nem  n>iT  \sh  nr  ib>bk  rvn  dnp  rrbn  bv2  Tbi  e^inn  join  rww 
, , .  jam  namrn  njnanno  tnnrw  ncn. 


INFINITE    SPACE  97 

as  much  as  the  other,  because  the  ratio  subsisting  between 
parts  is  also  the  ratio  between  their  totalities,  consequently 
infinity  is  impossible.126  A  more  modern  illustration  than 
that  of  heavenly  bodies  may  be  found  in  dollars  and  cents. 
A  dollar  is  to  a  cent  as  a  hundred  to  one — a  ratio  which 
holds  good  for  any  number  of  these  two  coins  ;  so  that  an 
infinite  number  of  dollars  will  be  a  hundred  times  as  much 
as  an  infinite  of  cents.  You  may  invent  many  more  such 
arguments  from  any  system  of  weights  and  measurements, 
and  you  will  get  the  same  conclusion,  contradicting  the 
fundamental  notion  of  the  infinite,  namely,  that  it  is  that 
greater  than  which  is  impossible. 

But  if  we  keep  our  previous  conclusions  clearly  in  mind, 
that  the  infinite,  existent  or  non-existent,  is  no  quantity, 
that  it  can  enter  into  no  quantitative  relationships,  it 
becomes  evident  first  of  all  that  a  thousand  years  from 
to-day  we  will  have  no  greater  infinite,  whether  of  temporal 
moments  or  spherical  revolutions,  than  now ;  for  the  terms 
1  greater '  and  *  less '  imply  a  quantitative  whole,  which 
infinity  is  not.  And,  secondly,  it  becomes  evident  that 
the  ratio  subsisting  between  parts  falls  off  as  soon  as  you 
enter  the  realm  of  the  infinite,  because  the  ratio  is  a  quan- 
titative relationship,  and  furthermore  because  the  ratio 
between  parts  which  is  to  hold  good  between  their  respec- 
tive totalities  is  by  no  means  similarly  applicable  to  the 
infinite,  which  is  not  a  quantitative  totality.  Thus  as  soon 
as  you  subject  the  infinite  to  mathematical  calculations  it 
slips  as  it  were  from  your  grasp,  and  what  you  are  really 
dealing  with  is  some  big  imaginary  finite  magnitude ;  but 
then,  after  you  have  drawn  your  conclusion,  you  exclaim 

126  Gersonides  adduces  the  same  argument  in  his  Milhamot,   p.  342. 
Similarly,  see  Spinoza,  /.  c. 

EF.  H 


98         PROBLEM    OF  SPACE    IN   JEWISH    PHILOSOPHY 

triumphantly  '  Eureka '.  Maimonides  therefore  remarks 
very  truly :  '  The  individual  accidents  that  have  passed  into 
non-existence  are  counted  and  represented  as  though  they 
were  still  in  existence,  and  as  though  they  ivere  things  with 
a  definite  beginning ;  this  imaginary  number  is  then  either 
increased  or  reduced!  For  it  is  evident  that  when  you  wish 
to  add  or  detract  you  deal  with  a  totality,  and,  as  Aristotle 
remarked,  the  total  and  the  infinite  are  mutually  contra- 
dictory. The  total  is  that  beyond  which  there  is  nothing, 
and  the  infinite  is  that  which  admits  of  no  beyond  alto- 
gether. Infinite  means  endless,  a  being  that  is  everywhere 
and  whose  existence,  being  immeasurable,  cannot  be  ex- 
pressed in  any  mathematical  formula,  and  cannot  be  the 
basis  of  any  mathematical  equation.127 

The  next  man  who  grappled  with  this  problem  was 
Gersonides.  I  cannot  allow  myself,  however,  to  omit  two 
casual  but  characteristic  remarks  of  two  men  living  before 
him,  Isaac  Ibn  Latif  and  Isaac  Israeli.  The  former  main- 
tains128 that  the  fact  that  our  perception  gives  us  the 
finite  only,  is  not  because  reality  is  finite,  but  because 
our    perceptive    organs    are   unable    to    see   the    infinite. 

127  See  Narboni,  who  expatiates  on  this  idea  which  Maimonides  puts 
very  briefly  and  suggestively. 

128  D^ya  a-i,  section  63 :  nnn»aty  i6x  ncw-nia  nnwxo  pa&n  noan 
nman  *a-iy  p£6a  ntnpan  ypwn  n&an  pi  rvbn  pj&  ly  nahro 
nmNXo  -iNtwrn  ?yn  p  nnbyw  *iy  naf>ini  nnn»ai  n»n»  N*fi  oa 
b>»b>  nip  mk>  nw^MMi  ivbn  nb  p«e>  itao  |wo  nab  ^w 
prnon  nonm  ipmrw  no  by  prno  dik>  mntw  n^nna  atn 
j>n!>  in**  i^bki  ohy^  waa^  pn»  «h  nnxn  h«  nnxn  inpm 
gallon  ab  swnnna  jnonn  xvoai  ,  .  .  n^an.    This  last  illustration 

Ibn  Latif  copied  literally  from  the  Guide,  I,  73,  prop.  10,  where  it  is  quoted 
from  a  certain  Book  of  Cones,  concerning  which  see  Steinschneider,  Heb. 
Ueber.,  p.  169.     It  is  also  cited  in  the  Or  Adonai,  p.  16  a. 


INFINITE    SPACE  99 

That  is  why  our  mind  does  posit  an  infinite.  Israeli,  on 
the  other  hand,  suggests 129  that  though  the  human  mind 
is  capable  of  drawing  the  line  and  the  surface  and  the  solid 
ad  infi7titum,  reality  consists  of  finite  and  definitely-shaped 
objects.  The  former,  Isaac  Ibn  Latif,  was  a  Kabbalist, 
moving  in  a  mysterious  boundless  atmosphere ;  the 
latter,  Isaac  Israeli,  was  a  scientist  busying  himself  with 
geometrical  figures. 

The  Maimonidean  suggestion  that  infinity  does  not 
denote  any  quantity,  served  as  a  starting-point  for 
Gersonides.  The  latter,  first  of  all,  establishes  that  any 
quantity,  whether  numerical  or  spatial,  is  by  its  nature 
limited.  This  is  a  genuine  Aristotelian  conception.  '  But ', 
says  Gersonides,  'we  do  not  admit  that  the  reason  why 
matter,  number,  and  magnitude  are  quantitatively  finite 
is  because  they  are  actual,  as  the  Philosopher  holds,  but 
because  of  the  intrinsic  nature  of  quantity,  the  proof  of 
this  being  that  number,  even  in  the  case  of  potential  objects 
like  time,  must  be  limited  nevertheless.' 130  Thus  quantity 
is  by  its  very  definition  finite.  On  the  other  hand,  infinity 
is  beyond  any  quantitative  description.  That  is  why  the 
current  definition  of  infinity  as  greater  than  the  greatest 
conceivable  body,  is  radically  wrong.  The  difference 
between  infinite  and  finite  is  not  merely  in  degree  but  in 
essence.  There  is  a  wide  unbridgeable  chasm  between  these 
two  natures.  The  infinite  is  irreducible  to  the  finite,  nor 
can  the  finite  be  enlarged  to  the  infinite.  Divide  and 
subdivide  the  unlimited,  if  that  is  at  all  possible,  and  you 

129  See  Yesod  Olam,  I,  2,  p.  5  a :  fetf  Hffl  Spam  1pm  nmTlW  N1H  JflT 
NSTCJ    OHO  TDK    D1K>  pK    ^3N    IpTl    pN    1J?    I^SN    .1381103    IWDrfo 

naioni  n^an  byz  t6x  bwzi. 

130  Milhamot,  pp.  336  ff. 

H  3 


TOO        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

are  still  within  the  realm  of  the  unlimited.131  On  the  other 
hand,  even  if  you  were  granted  eternal  life,  and  were  to  be 
engaged  all  your  time  in  putting  together  particles  of 
space,  you  would  not  step  over  the  boundary  of  the  finite. 
1  Just  as  a  point  will  remain  a  point  no  matter  how  much 
you  multiply  it,  because  out  of  indivisibles  you  cannot 
get  anything  else  than  the  indivisible ;  so  magnitude  will 
always  remain  magnitude,  no  matter  how  much  you  may 
multiply  it;  for  it  is  infinitely  finite  with  all augmentation.' U2 
The  latter  is  a  very  pregnant  saying :  '  Magnitude  is  in- 
finitely finite.'  The  infinite  is  not  a  product  of  an  incon- 
ceivable number  of  finite  spaces.  It  does  not  differ  from 
the  finite  quantitatively,  but  qualitatively ;  it  is  altogether 
sui  generis.  What  that  essential  quality  is,  is  not  quite 
clearly  expressed.  But  the  meaning  seems  to  be  this, 
namely,  the  removal  in  our  thought  of  all  quantitative 
determinations  and  limits.  Focus  your  attention  on  the 
spatial  fact  itself,  purely  as  a  simultaneous  co-existence 
without  thinking  of  how  far  it  is  spatial,  or  on  time  purely 
as  a  successive  flux,  without  thinking  of  the  length  of  its 
duration  ;  just  as  you  may  think  of  colour  without  regard  to 
its  space  limits,  and  you  have  the  notion  of  the  infinite. 
Spatial  infinity  then  might  be  defined  as  the  representation 

131  Thus  he  argues  on  p.  406,  on  the  basis  of  this  idea  which  can  be 
expressed  in  the  equation  —  =  « ,  that  if  we  divide  infinite  time  into  a  finite 
number  of  times,  we  find  ourselves  in  a  baffling  dilemma.  The  whole  is 
naturally  bigger  than  the  part,  but  the  part  of  an  infinite  is  likewise  infinite, 
how  then  can  we  conceive  of  two  infinites,  one  greater  than  the  other? 
Hence  time  is  finite.  Comp.  also  his  argument  from  the  '  Lunar  Eclipse '  on 
P-  342- 

132  ibid.,  345:  rfbm  bvn  n^an  jnb  Ton  (i.e.  magnitude)  wn  »a 


INFINITE    SPACE  IOl 

of  the  space-fact  itself  without  regard  to  its  quantitative 
aspect.  This  conception  of  the  infinite  is  novel  and  inter- 
esting ;  it  justifies  the  possibility  of  such  a  notion  without 
involving  oneself  in  numerous  antinomies  that  arise  out 
of  a  misunderstanding ;  and  the  emphasis  that  it  lays  on 
the  idea  that  the  infinite  is  not  merely  something  greater 
than  the  greatest  conceivable  finite,  marks  an  advance 
in  history  of  the  notion.  The  reader  will  note  that  Professor 
Fullerton  recently  urged  exactly  the  same  point,  and  on 
the  basis  of  very  much  similar  arguments.133 

But  conception  is  one  thing,  and  reality  another.  Such 
an  abstract  idea  of  the  infinite  is,  like  all  abstractions,  a 
purely  mental  fact.  In  reality,  everything  is  limited  and 
can  be  represented  in  a  definite  quantitative  form;    and 


133  See  his  Conception  of  the  Infinite,  ch.  2.  I  could  hardly  suspect 
Professor  Fullerton  of  having  read  the  Mil/jamot,  but  there  is  a  very 
famous  thinker  in  the  history  of  modern  philosophy  who  takes  a  similar 
view  on  the  meaning  of  the  infinite,  and  about  whom  such  a  suspicion  might 
be  ventured,  I  mean  Baruch  Spinoza.  In  Part  I  of  his  Ethics  he  lays  down 
the  proposition  that  substance  absolutely  infinite  is  indivisible ;  and  antici- 
pating some  difficulty  on  the  part  of  the  reader  to  grasp  the  meaning  of  this 
paradoxical  statement,  he  seeks  to  make  it  comprehensible  (see  note  to 
prop.  xv).  But  our  study  of  Gersonides  makes  the  meaning  clear.  The 
infinite  is  merely  'the  representation  of  the  space-fact  itself  without  regard 
to  its  quantitative  aspect',  and  is  therefore  indivisible.  Only  a  definite 
quantity  can  be  divided ;  spatiality  as  such  is  found  in  the  same  degree 
in  a  grain  of  sand  and  in  the  immeasurable  ocean.  The  infinite  designates 
space  as  a  quality  of  matter  and  consequently  suffers  no  diminution  by  any 
process  of  quantitative  division.  That  this  indeed  is  Spinoza's  meaning  is 
evident  from  his  definition  of  eternity  which  is  simply  infinity  in  succession, 
namely,  as  •  existence  itself  in  so  far  as  it  is  conceived  necessarily  to  follow 
solely  from  the  definition  of  that  which  is  eternal'  and  as  distinguished  from 
beginningless  and  endless  continuity.  Be  it  also  remarked  that  from  this 
standpoint  the  distinction  between  the  infinite  and  the  infinitesimal  dis- 
appears, for  the  degree  of  largeness  or  smallness  of  matter  plays  no  part 
in  this  conception  of  the  infinite. 


102        PROBLEM    OF   SPACE  IN   JEWISH    PHILOSOPHY 

space  is  bounded  with  the  bounds  of  the  universe.134  Yet 
there  is  one  sense  in  which  infinity  can  be  said  to  be  real, 
and  that  is  in  process.  There  is  no  end  to  the  mental 
power  of  augmentation  and  diminution.  There  is  no  final 
term  to  a  convergent  series  enlarging  space  by  a  certain 
unit,  nor  to  a  divergent  series  lessening  space  by  a  certain 
unit.  Such  a  series  may  go  on  ad  infinitum,  though  every 
term  in  that  series  is  but  a  limited  quantity,  and  gives  us 
a  sum  total  of  a  limited  quantity.  All  this  is  because 
the  human  mind  has  acquired  the  ability  to  add  and 
detract,  and  not  having  experienced  anything  that  refuses 
addition  or  subtraction,  it  can  conceive  of  no  limit  to  that 
ability.  But  by  addition  and  subtraction  we  can  get 
nothing  but  finite  results,  so  that  this  mental  ability  implies 
two  apparently  diametrically  opposite  things,  namely,  an 
infinite  process  with  finite  results.  Indeed,  the  very  exercise 
of  this  ability  precludes  any  infinite  result,  for  then  the 
process  would  come  to  an  end,  inasmuch  as  nothing  can 
be  added  to  the  infinite,  and  thus  the  process  would  no 
more  be  infinite.  Yet  the  reader  will  ask,  if  infinite  addition 
means  anything  at  all,  it  means  that  there  is  no  end  to  the 
process  of  adding,  consequently  there  is  no  end  to  that 
which  is  added.  But,  as  I  have  shown,  if  you  analyse  the 
term  infinite  addition,  you  find  that  it  means  that  the 
additional  process  has  no  limit  beyond  which  it  cannot  be 
carried,  but  an  infinite  result  which  cannot  be  augmented 
any  more  must  set  up  a  limit  to  the  process.  Hence  the 
inference  from  infinity  of  process  to  infinity  of  state  is 
134  '•  c-,  P-  339-     See  also  p.  386  :  DIKrl  TOTP  TO  b   pN  H3H  &3» 

mrw  pry  t6  cpm  onm  dp  bin  pnx  bz  Dixn  tot  vb\  pra 
«bi  mpn  vb  wkv  vbmnn  mjjn  ba  nbiyn  nta  102  d*wi  ddin 
rvb  totp  toi  »£d. 


INFINITE    SPACE  103 

unjustifiable.  That  is  why  'magnitude  is  infinitely 
finite  \ 

This  explanation  of  Gersonides  differs  from  the  theory 
of  potentiality  as  developed  by  Aristotle.  He  cautions 135 
the  reader  not  to  understand  by  infinite  divisibility  or 
augmentation  that  a  body  harbours  a  possibility  to  be 
reduced  into  an  infinitesimal  or  enlarged  into  an  infinite, 
because  that  involves  a  misunderstanding  of  the  infinite 
which  really  cannot  be  attained  by  means  of  the  finite. 
All  that  is  meant  is,  that  a  body,  being  extended,  must  be 
divisible ;  and  inasmuch  as  it  is  a  physical  law  that  a  body 
cannot  be  destroyed  by  division,  every  part  must  be  further 
divisible.  Similarly  with  augmentation,  because  any  dimen- 
sional body  has  the  quality  of  being  enlarged.  Thus  two 
series  set  in,  one  convergent  (1,  2,  3,  4,  5,  &c.)  and  the 
other  divergent  (1,  \,  i,  |,  fo  &c).  Both  series  run  ad 
infinitum-,  and  it  is  the  condition  of  such  a  series,  as 
has  been  shown,  that  no  infinite  term  can  be  reached. 
Gersonides  was  more  consistent  than  Aristotle  in  making 
no  discrimination  between  infinite  divisibility  and  infinite 
augmentation. 

Thus  Gersonides's  standpoint  makes  a  genuine  con- 
tribution to  the  history  of  this  difficult  problem.  In 
completely  severing  the  notion  of  the  infinite  from  any 
quantitative  relations,  and  in  showing  how  infinity  of 
process  may,  and  indeed  must,  go  hand  in  hand  with 
finitude  of  state,  Gersonides  may  still  claim  attention  from 
modern  thought.  We  will  now  pass  to  the  next  man, 
Hasdai  Crescas. 

The  reader  perhaps  expects  from  Crescas  a  defence  of 
the  theory  of  the  infinite ;  the  expectation  being  based  on 
135  Ibid.,  334. 


104        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

two  reasons :  first,  Crescas  was  the  first  in  the  history  of 
Jewish  thought  to  challenge  Aristotelianism,  and  thus 
might  have  been  led  to  renounce  also  the  Aristotelian 
theory  of  the  finitude  of  things ;  secondly,  Crescas  was, 
as  we  have  seen,  the  first  Jewish  thinker  to  postulate  pure 
space  outside  of  and  beyond  the  confines  of  the  universe, 
thus  space  at  least  must  be  limitless.  Well,  the  reader  is 
not  altogether  wrong  in  his  expectation,  though  not  quite 
right.  It  is  true  that  Crescas  took  issue  with  Aristotle 
on  the  subject  of  the  infinite,  and  apparently  he  explicitly 
states  that  space  is  unlimited.  '  It  has  been  explained  ', 
he  remarks  in  one  place,  'that  outside  the  world  there 
must  be  either  a  full  or  a  void,  and  that  boundless  dimen- 
sionality must  exist.  And  even  if  it  were  non-existent, 
we  would  have  to  posit  it,  just  as  the  geometrician  makes 
use  of  such  a  concept  in  the  definition  of  parallel  lines  and 
other  fundamental  terms.' 136  The  latter  comparison,  how- 
ever, already  casts  some  suspicion  on  the  author's  meaning. 
The  geometrician  does  not  assume  the  infinite  as  a  neces- 
sary fact,  but  as  a  hypothetical  nature  which  must  conform 
if  real  to  the  general  laws  and  conditions  of  geometrical 
figures.  It  is  only  in  this  sense  that  we  say  two  parallel 
lines  are  infinitely  equidistant  from  one  another.  If  now 
you  make  further  investigation  into  the  author's  real 
opinion,  you  will  find  that  Crescas  at  bottom  adopted  the 
view-point  that  was  elaborated  by  Gersonides. 

I  said  that  Crescas  took  issue  with  Aristotle  on  the 
subject  of  the  infinite.  Indeed,  he  attacked  all  arguments 
of  the  Greek  philosopher,  as  well  as  other  arguments  that 
were  advanced  in  negating  the  idea  later  by  Arabian 
sch5lastics.  An  exposition  of  this  discussion  in  detail 
136  'n  TIN,  p.  16b. 


INFINITE    SPACE  105 

would  really  lead  me  away  into  the  infinite,  I  mean  outside 
the  limits  of  this  work.  I  shall  select  two  arguments  which 
Shem  Tob,  the  commentator  of  Maimonides,137  thinks  the 
most  convincing  proofs  against  the  existence  of  the  infinite, 
but  which  Crescas  repudiated.  These  two  arguments  are 
absolutely  necessary  for  our  general  problem,  because  they 
touch  the  fundamental  question  whether  the  mathematical 
laws  of  space  admit  of  limitless  extension. 

The  first  argument  Crescas  quotes  from  Tabrizi,138  an 
Arabian  commentator   of  Maimonides,  and   is   called    an 
argument  from  superposition.     Let  AB  represent  a  line 
A  C B 

running  ad  infinitum.  Mark  off  a  certain  distance  from  A 
and  call  it  C.  Thus  we  have  here  two  infinite  lines  AB  and 
CB.  Now  let  the  two  lines  so  coincide  that  C  falls  on  A. 
Evidently  the  line  CB  which  is  shorter  by  A  C  will  terminate 
some  distance  from  AB.  Consequently  one  infinity  is 
greater  than  another,  which  is  absurd.  Hence  infinity  is 
impossible.  The  reader  will  recall  this  argument  from 
a  Jewish  source,  namely,  from  Bahya,  who  lived  some  time 
before  Tabrizi.  But  it  is  evident  that  the  author  of  this 
proof  juggles  with  the  word  infinite,  and  Crescas  exposes 
that  fact. 

Altogether,  Crescas  remarks,139  it  is  not  exact  to  say 

137  See  Shem  Tob's  Commentary  on  the  Guide,  II,  Introd.,  prop.  1. 

188  'n  TIN,  pp.  5  a  and  15  a.  The  argument  is  called  in  Hebrew  DSID 
nipTinnn.  The  translation  of  Tabrizi's  Commentary  on  the  twenty-five 
propositions  forming  the  introduction  to  Part  II,  was  printed  under  the  title 
iT-HD.TO  nW3  nVp  together  with  \TQS\  h$W  TYbtW.  See  also  Stein- 
schneider,  Heb.  Ueber.,  p.  207. 

183  'n  nix,  p.  67b.:  rwna  vb  n'aane  hna  wn  ifaaw  unwa  »a 
bin  WWi  Dtr  bw  vh  n"n2n^  iNiinn  133P  n'zzb  nw  Nine  u 
n"23E  ?Dp  W  bvn  n"2in  nsins^  lamo  p«»  in  rvev- 


106        PROBLEM    OF    SPACE    IN   JEWISH    PHILOSOPHY 

that  one  infinity  cannot  be  greater  than  another,  the  fact  is 
that  it  cannot  also  equal  another.  Not  only  inequality,  but 
also  equality,  is  inapplicable  to  infinities.  For  even  when 
we  say  that  a  thing  equals,  we  have  in  our  mind  a  whole 
quantum,  in  other  words,  a  limited  nature.  Hence  it  is  just 
as  absurd  to  maintain  that  AB  equals,  as  to  maintain  that 
it  is  greater  than  CB,  for  in  either  case  we  only  say  that 
we  are  dealing  with  the  unlimited ;  in  our  mind,  however, 
we  have  a  definite  measured  amount  which  we  try  to 
compare  with  another  equal  or  unequal  amount.  All  mathe- 
matical considerations,  all  signs  of  equality  and  inequality, 
must  be  dropped  entirely,  if  we  really  wish  to  conceive  the 
endless.  Else  we  are  like  the  fabulous  peacock  that  sought 
to  escape  its  feet  by  flying. 

Having  this  idea  clearly  in  mind,  we  will  find  that  the 
whole  difficulty  with  this  argument  disappears.  Let  us 
take  an  example  from  time  which  is  supposedly  beginning- 
less.  Up  to  now  we  have  a  series  of  moments  infinite  as 
to  beginning,  but  limited  by  this  present  moment.  A  day 
passes  by  and  a  number  of  moments  are  added  to  the  past. 
It  does  not  mean,  however,  that  the  infinite  has  been 
'  increased  ',  for  this  would  suggest  that  we  had  a  fixed 
calculable  number  of  moments  which  we  really  did  not 
have.  We  have  a  case  of  addition,  but  we  cannot  reduce 
it  to  a  mathematical  equation.  What  are  you  going  to  add 
it  to  ?  You  are  dealing  here  with  unmathematical  notions 
or  metamathematical,  if  you  will,  and  you  have  no  right  to 

He  thus  overthrows  Gersonides's  argument  against  infinity  from  the  infinite 
number  of  lunar  eclipses,  which  not  being  greater,  must  be  equal  to,  and 
coincident  with,  the  infinite  number  of  non-eclipses.  According  to  Crescas 
one  infinity  can  neither  be  greater  nor  equal  to  another,  for  it  is  altogether 
beyond  the  category  of  number.  The  whole  passage  is  found  verbatim  in 
Abrabancl's  QTI^N  Dl^SE,  IX,  7.     See  also  above,  end  of  ch.  2. 


INFINITE    SPACE  107 

subject  them  to  mathematical  treatment.  Similarly,  you 
have  drawn  a  line  in  space  from  this  point  ad  infinitum, 
a  yard  further  you  have  drawn  a  similar  line.  Both  lines 
represent  only  an  incomplete,  so  to  speak,  or  unrealized 
infinite  which  must  be  endless  as  well  as  beginningless, 
leading  from  eternity  to  eternity.  At  any  rate,  all  you 
have  is  a  certain  distance  which  might  be  added  to  the 
infinite  line  B.  But  to  draw  hastily  a  mathematical  equation 
and  to  seek  to  get  the  net  result,  is  to  assume  an  imaginary 
finite  line,  or  to  have  a  wrong  notion  of  what  endlessness 
means. 

The  second  argument  is  as  follows  : uo  If  space  is  infinite 
we  may  select  any  point  as  a  centre  through  which  diameters 
run  ad  infinitum.  The  distance  between  any  two  diameters 
which  form  an  angle  at  the  centre  becomes  wider  and  wider 
until  the  intercepted  arc  would  be  infinite.  Now  the  diffi- 
culty is  twofold.  First,  if  we  imagine  this  infinite  space 
to  have  a  circular  movement,  how  would  the  moving  dia- 
meter cross  this  infinite  intercepted  arc  ?  An  infinity  is  just 
that  which  cannot  be  crossed  over.  Secondly,  how  can  the 
arc  be  infinite  when  it  is  limited  by  the  two  diameters  ?  and 
if  it  is  not  limited  by  them,  the  diameters  must  be  finite. 
And  if  they  are  finite,  the  intercepted  arc  is  naturally 
finite  too. 

Now,  first,  Crescas  removes  the  objection  from  motion. 
It  is  inconceivable  how  an  infinite  body  could  move.  To 
move  means  to  leave  an  occupied  place  and  to  occupy  an 
unoccupied  place,  but  no  place  is  free  from  the  infinite. 
He  now  turns  to  the  second  difficulty.     An  intercepted  arc 

140  'n  TIN,  pp.  7  a,  16  b.  This  argument  is  in  the  main  identical  with 
Tabrizi's 'argument  from  scales',  ""D^DD  DS1D.  Cf.  J.  ft,  p.  5  b.  Comp. 
also  Spinoza's  Ethics,  part  I,  prop,  xv,  note. 


Io8        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

between  two  infinite  diameters  would  eventually  be  infinite. 
But  if  it  is  infinite,  how  is  it  limited  by  the  two  diameters, 
and  if  it  is  unlimited  by  them,  they  must  be  finite.  To 
this  Crescas  replies,  an  infinite  line  does  not  mean  one  that 
has  infinite  extent  between  its  ends — a  meaning  which  is 
of  course  contradictory  and  nonsensical.  Similarly,  it  is 
absurd  to  look  on  this  diameter  for  a  point  which  will  be 
an  infinite  distance  from  the  centre ;  and  inasmuch  as  the 
arc  could  be  infinite  only  at  such  a  point,  it  is  evident  that 
an  infinite  arc  is  impossible.  What  then  do  we  mean  by 
1  the  infinite  diameter '  ?  Just  this,  that  there  is  no  limit  to 
the  possibility  of  extending  the  line,  because  space  itself 
cannot  be  conceived  to  have  limits  ;  that  it  can  be  infinitely 
prolonged  and  nevertheless  preserve  its  finite  nature.  This 
fact  may  at  first  seem  strange,  but  it  is  no  more  strange, 
says  Crescas,  than  the  fact  cited  in  the  Book  of  Cones,ul 
that  two  lines  starting  at  a  distance  from  one  another,  and 
drawing  nearer  while  they  go  on,  never  come  in  contact,  even 
though  you  may  prolong  them  ad  infinitum.  Infinity  then 
denotes  a  process  which  may  be  perpetually  carried  on 
without  breaking  up  the  integral  nature  of  the  object,  just 
as  finitude  denotes  a  limit  which  a  certain  process  cannot 
surpass  without  destroying  the  peculiar  nature  of  the  object, 
as  when  we  say  that  a  body  is  only  finitely  divisible.  Thus 
the  diameter  is  infinite  because  it  can  endlessly  be  extended, 
though  it  always  preserves  its  finiteness,  though  it  never 
reaches  a  point  which  is  at  a  boundless  distance  from  the 
centre,  and  so  never  possibly  intercepts  an  infinite  arc. 
The  reader  will  recall  the  pregnant  saying,  '  Magnitude  is 
infinitely  finite '.  The  key-note  of  this  whole  discussion 
is  that  there  is  an  infinite  process,  which  naturally  implies 
finite  results. 

141  See  above,  note  128. 


INFINITE    SPACE  109 

Thus  there  are  two  fundamental  notions  about  the 
infinite  which  stand  out  very  clearly  from  these  two  argu- 
ments. The  first  argument  shows  that  infinity  is  in  nowise 
reducible  to  terms  of  finitude  and  quantity,  and  vice  versa. 
Hence  the  idea  that  we  conceive  the  infinite  by  means  of 
a  successive  synthesis  of  finites  is  erroneous.  We  may 
delve  deep  into  the  bottomless  abyss,  we  may  soar  on  our 
imagination  to  the  dreary  regions  of  pure  space,  we  may 
make  a  life-long,  or  an  eternity-long,  successive  synthesis, 
but  we  will  still  find  ourselves  much  within  the  boundaries 
of  the  finite,  simply  because  finite  plus  finite  equals  finite. 
It  is  not  by  widening  limits,  but  by  removing  limits,  by 
thinking  away  all  quantitative  determinations,  that  we  are 
allowed  a  glimpse  of  the  infinite. 

The  second  argument  obviates  an  objection  from  the 
reader,  namely,  if  space  can  be  endlessly  enlarged,  it  must 
finally  be  endlessly  large.  The  word  '  finally '  is  not  appro- 
priate. Infinity  denotes  a  process  which  is  endless, 
consequently  it  has  no  final  term.  Hence  there  can  be  no 
infinite  state  or  infinite  result,  because  that  would  be  a  final 
term.  The  second  argument  then  brings  out  the  comple- 
mentary idea  that  there  is  a  logical  harmony  between 
infinity  of  process  and  finitude  of  results. 

Thus  we  have  seen  how  this  conception  as  a  whole  was 
first  faintly  suggested  by  Maimonides,  given  prominence 
by  Narboni,  elaborated  and  crystallized  by  Gersonides,  and 
finally  clarified  by  Hasdai  Crescas.  It  may,  therefore,  be 
justly  called  the  view  of  infinity  of  mediaeval  Jewish  philo- 
sophy— a  view  that  may  claim  even  at  the  present  day  the 
serious  attention  of  the  student  who  is  perplexed  by  the 
tangle  of  numerous  contradictions  and  antinomies  which 
this  problem  presents. 


ho      problem  of  space  in  jewish  philosophy 

Conclusion 

A  brief  rfaumd  of  the  chief  points  in  the  preceding 
discussion  is  now  in  order.  I  shall  select  the  four  central 
problems  that  have  occupied  our  attention  so  far,  and 
examine  the  solution  offered  by  the  mediaeval  Jewish 
thinkers.  These  problems  are :  (i)  the  reality  of  empirical 
space,  (%)  the  infinite  divisibility  of  space,  (3)  the  existence 
of  absolute  space,  and  (4)  the  infinity  of  space. 

(1)  In  Jewish  philosophy  space  is  conceived  as  an 
objective  reality.  By  '  reality '  I  understand  the  existence 
of  a  thing  in  the  objective  world  independent  of  our  per- 
ception. The  mediaeval  mind  in  general  saw  no  problem 
in  the  reality  of  space.  One  might  have  disputed  on  how 
many  angels  could  stand  tip-toe  on  a  pin-head,  but  that 
the  pin-head  exists  with  a  certain  magnitude  of  extension, 
no  one  entertained  any  doubt.  It  is  only  the  modern 
mind,  hypersophisticated,  philosophically  gone  astray,  that 
nervously  asks  whether  this  vast  extension  above  and  below 
and  around  us  is  not  a  mere  illusion.  Not  only  did  the 
Jewish  thinkers  affirm  the  independent  existence  of  space, 
but  some  even  went  so  far  as  to  take  a  geometric  view  of 
things  and  conceive  the  corporeal  essence  in  terms  of  space. 
Matter,  they  maintained,  is  not  merely  that  which  takes 
up  space,  but  it  is  space.  All  other  characteristics  that 
a  certain  object  may  possess  are  altogether  unimportant 
for  a  pure  conception  of  matter.  A  material  object,  ac- 
cording to  these  thinkers,  may  be  defined  as  a  limited 
magnitude  of  space  that  possesses  certain  qualities.  Thus 
space  and  matter  are  synonymous  terms.  Other  thinkers 
are  less  radical,  and  put  space  in  the  category  of  qualities. 
Corporeality  means  for  them  some  mysterious  substrate, 


INFINITE    SPACE  III 

the  conception  of  which  requires  no  space  determinatives. 
Yet  in  reality,  all  admit,  space  is  inseparable  from  matter. 

(a)  But  if  unextended  matter  is  an  impossibility,  it  is 
evident  that  the  Arabian  atomic  hypothesis,  which  reduces 
matter  to  ultimate  non-magnitudinal  parts,  must  be  re- 
jected. A  non-magnitudinal  part  is  in  the  first  place 
impossible  in  itself,  and  secondly,  how  could  it  produce 
extension  by  combining  with  a  similar  part?  A  point  is 
zero  of  extension,  and  you  may  add  zeros  ad  infinitum 
without  ever  getting  a  number.  Besides,  the  word  !  com- 
bine '  itself,  if  it  is  meant  in  a  physical  and  not  in  a  chemical 
sense,  which  is  irrelevant  in  this  connexion,  implies  a 
limit  coming  in  contact  with  another  limit,  and  a  limit 
is  a  point  before  which  there  is  a  point  which  is  no  limit. 
In  short,  combination  implies  that  that  which  combines  is 
an  aggregate  of  points,  and  consequently  extended.  Hence 
the  idea  that  matter  is  composed  of  ultimate  spaceless 
parts  must  be  abandoned.  The  truth  is,  that  no  matter 
how  much  you  may  divide  and  subdivide  a  piece  of  matter, 
you  will  always  get  something  that  is  further  divisible. 
Of  course,  practically,  you  will  eventually  reach  a  minimum 
sensibile ;  theoretically,  however,  nothing  prevents  us  from 
continuing  with  our  process  of  division.  Extension  means 
1  alongsidedness  of  parts ',  and  hence  divisibility.  Conse- 
quently, as  long  as  you  have  matter  you  have  divisibility. 
Therefore  anything,  however  small  and  minute,  can  be 
divided  ad  infinitum.  But  here  a  dreadful  gap  opens  up 
wide  before  us.  If  things  are  infinitely  divisible,  they  must 
have  an  infinite  number  of  parts,  but  how  can  a  finite 
object  contain  an  infinite  number  of  parts  ?  How  can  we 
move  over  even  the  smallest  distance?  And  how  could 
Achilles  overtake  the  tortoise  when  the  distance  between 


112        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

them  is  infinitely  divisible,  and  each  half  of  the  distance 
that  Achilles  covers  leaves  another  half  between  them, 
growing  smaller  and  smaller  to  be  sure,  but  never  becoming 
zero?  Indeed,  one  might  ask  how  they  can  both  begin 
to  move,  since  the  very  first  step,  even  that  of  the  tortoise, 
involves  a  crossing  of  an  infinite  abyss?  The  fourth  point, 
on  the  infinity  of  space,  will  give  an  answer  to  these 
questions  also. 

(3)  So  much  for  empirical  space,  or  concrete  extensity. 
.  This  is  undeniably  real,  as  real  as  matter  of  which  it  is 
the  distinguishing  characteristic.  But  is  there  such  a  thing 
as  pure  space,  mere  dimensionality  outside  of  and  beyond 
the  world  of  matter?  Here  opinions  differed,  the  majority 
being  against  the  existence  of  a  void.  In  accepting  the 
Aristotelian  notion  of  space  as  '  the  inner  limit  of  the 
containing  body',  or  a  mere  relation  of  contiguity  between 
two  objects,  the  Jewish  thinkers  had  to  endorse  the 
exclusion  of  the  possibility  of  pure  space.  For  if  by  space, 
as  distinguished  from  concrete  extension,  is  meant  merely 
contiguity,  it  is  evident  that  where  there  are  no  bodies, 
there  can  be  no  space.  This  is  precisely  the  Leibnizian 
position.  Yet  there  is  this  critical  remark  to  be  made. 
Such  a  position  might  indeed  explain  the  possibility  of 
conceiving  the  vanishing  of  the  space  order,  with  the 
annihilation  of  the  world  of  matter.  But  if  this  relation- 
ship of  contiguity  is  to  supplant  the  notion  of  space,  by 
inheriting  also  its  apodictic  certainty ;  I  mean,  if  the  mind 
necessarily  postulates  such  contiguity  in  connexion  with 
matter;  if  an  object  cannot  be  conceived  to  exist  out- 
side of  such  relationship,  the  question  may  be  asked, 
how  is  the  universe  as  a  whole  conceivable  without 
such   relations?     What,   if  pure  space  is  denied,  is  con- 


INFINITE    SPACE  113 

tiguous  with  the  confines  of  the  world  ?  By  what  is 
matter  limited  ?  Indeed,  such  an  objection,  we  have 
seen,  was  raised  against  the  Aristotelian  theory  of  the 
existence  of  a  sphere  which  is  all-containing  and  not  con- 
tained. But  the  Jewish  thinkers  who  negated  the  void 
would  have  flatly  refused  to  confer  'apodictic  certainty' 
on  the  relationship  of  contiguity.  Some,  it  is  true,  were 
puzzled  by  the  question :  What  is  there  beyond  ?  And 
after  they  have  proved  by  a  series  of  arguments,  to  their 
own  satisfaction,  that  space  has  limits  and  there  is  nothing 
beyond,  they  suddenly  started  at  their  own  expression  : 
Yes,  but  does  not  the  word  '  beyond '  suggest  a  spatial 
background  ?  The  whole  puzzle,  however,  was  solved  very 
truly  by  Abrabanel.  The  mind  constantly  receives  spatial 
impressions  from  the  external  world,  so  that  it  has  acquired 
a  habit  to  consider  things  in  spatial  relations.  Hence 
a  solitary  object  that  is  shorn  of  these  relations,  is  not 
easily  conceivable,  but  it  is  not  inconceivable.  The  human 
mind  can  transcend  this  habit  and  conceive  of  a  finite 
totality  which  stands  in  no  spatial  relations  with  any- 
thing else. 

(4)  And  so  I  come  to  the  last  point  in  our  discussion. 
We  saw  in  connexion  with  the  idea  of  the  void,  that  the 
finitude  of  space  is  held  by  the  majority  of  Jewish  thinkers. 
But  infinite  space  presents  a  problem  of  its  own.  On  the 
one  hand  many  mathematical  demonstrations  might  be 
made  showing  the  impossibility  of  infinity;  on  the  other 
hand,  infinity  seems  to  be  a  positive  fact  of  experience. 
There  can  be  no  limit  to  the  possibility  of  enlarging  an 
object,  just  as  we  have  seen  that  there  can  be  no  limit 
to  the  possibility  of  dividing  a  certain  object.  And  if  that 
is  so,  will  not  these  two  antithetical  processes  evolve  two 
EF.*  I 


114        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

bodies,  one  infinitely  large,  and  the  other  infinitely  small  ? 
Jewish  philosophy  has  this  to  say  on  this  serious  difficulty. 
It  is  contradictory  to  speak  of  a  body  that  is  'infinitely 
large '  or  '  infinitely  small '.  The  terms  •  large '  and  '  small ' 
denote  quantity,  they  present  to  our  mind  a  definite  limited 
magnitude ;  and  infinity  means  limitless.  Infinity,  above 
all,  must  be  absolutely  distinguished  from  quantity;  it  is 
just  by  the  removal  of  quantity  that  you  conceive  the 
infinite.  And  the  fundamental  error  in  the  first  Kantian 
antinomy  is  just  this :  that  infinity  is  conceived  as  a  suc- 
cessive synthesis  of  parts,  whereas  true  infinity  refuses 
being  measured  because  it  is  just  the  reverse  of  measure, 
and  excludes  the  notion  of  a  part  because  it  is  indivisible 
as  well  as  unaugmentable,  being  no  definite  magnitude, 
and  is  not  obtained  by  a  series  of  successive  syntheses, 
because  you  may  choose  the  greatest  conceivable  magnitude 
and  multiply  it  by  the  greatest  imaginable  number,  and 
what  you  will  have  will  be  a  finite  object  as  finite  as  a 
grain  of  sand  and  a  blade  of  grass.  Finite  plus  finite 
equals  finite. 

What  then  does  infinity  mean  ?  It  represents  a  process 
that  may  be  carried  endlessly  without  destroying  the 
object ;  just  as  finitude  represents  such  a  process  that  will 
ultimately  reach  a  limit,  the  crossing  of  which  would  spell 
injury  to  the  object.  It  is  in  this  sense  that  we  say  matter 
is  infinitely  augmentable,  meaning  that  we  can  enlarge  and 
further  enlarge  a  given  magnitude  of  matter  ad  infinitum, 
without  ever  producing  an  infinite  magnitude,  because  that 
would  mean  the  loss  of  matter  which  is  by  nature  limited 
and  circumscribed.  Indeed,  it  is  absurd  to  believe  that 
such  an  infinite  will  eventually  be  reached,  because  then 
the  process  will  cease,  infinity  being  unaugmentable,  and 


INFINITE    SPACE  115 

the  process  will  therefore  be  finite.  Hence  an  infinite  pro- 
cess presupposes  finite  results,  and  as  one  Jewish  thinker 
cleverly  remarked :  Matter  is  infinitely  finite.  Similarly, 
infinite  divisibility  denotes  that  the  process  of  division  may 
be  carried  on  theoretically  ad  infinitum,  without  bringing 
about  the  loss  of  the  object.  Yet  this  endless  process  never 
produces  the  infinitesimal,  because  that  would  involve  the 
end  of  the  process.  But  does  not  this  mean,  the  reader 
will  ask,  that  we  could  resolve  a  piece  of  matter  into  an 
infinite  number  of  parts?  No;  first  of  all  an  infinite 
number  is  a  contradiction  of  terms,  and,  secondly,  if  such 
an  infinite  number  could  possibly  be  attained  the  process  of 
division  would  cease,  but  it  is  endless.  Hence  while  each 
part  becomes  smaller  and  the  number  of  parts  greater,  they 
cannot  both  overleap  the  boundaries  of  the  finite.  Thus 
Zeno's  puzzles  vanish  like  shadows  in  the  light.  We  do 
not  move  over  infinities,  and  Achilles  can  easily  overtake 
the  tortoise.  What  we  have  to  bear  in  mind  is  only  this, 
that  infinity  is  a  process,  not  a  state. 

Thus  I  have  outlined  briefly  the  Jewish  standpoint  in 
the  problem  of  space,  and  I  might  conclude  here  perfectly 
well.  Yet  I  should  like  to  discuss  one  more  point  with 
the  reader  before  we  part.  It  is  the  Jewish  empirical  view 
versus  the  modern  doctrine  of  the  subjectivity  of  space. 
I  fear  that  many  a  Kantian  reader  will  leave  this  volume — 
if  he  looks  at  it  at  all — with  a  smile :  Objectivity  of  space, 
Mediaevalism !  Yet  I  believe  that  the  phenomenalistic 
theory  has  hindered  rather  than  helped  man  in  his  desire 
to  know  his  whereabouts,  so  as  to  adjust  the  interrelations 
in  the  best  possible  manner.  Kant  did  not  explain  things, 
but  transformed  the  world  into  a  dreadful  yawning  abyss 
and  called  it  Noumenon.     He  argued  that  we  can  mentally 

I  2 


Il6        PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

annihilate  and  think  away  matter,  but  we  cannot  think 
away  space,  consequently  space  is  a  necessity  of  thought. 
But  for  myself,  I  cannot  see  how  we  can  think  away  matter. 
Of  course  we  can  stop  thinking  at  all,  then  we  have  thought 
away  space,  also ;  but  to  think  and  not  to  think  of  things  is 
absurd.  When  we  think,  of  course  we  think  something  and 
about  something.  Objects  of  experience  are  the  contents 
of  our  thought ;  think  away  those  objects,  and  thought 
becomes  meaningless.  And  as  for  space  being  a  necessity 
of  the  mind,  Abrabanel,  we  have  seen,  explains  it  very 
clearly.  It  is  a  habit  contracted  by  the  mind  under  the 
pressure  of  constant  spatial  experience.  Had  the  human 
mind  been  born  in  a  spaceless  universe,  spacelessness  would 
have  become  a  necessity  of  thought.  For  what  is  con- 
sciousness if  not  the  manifold  impresses  of  external  stimuli  ? 
Hence  the  very  idea  that  space  is  a  necessity  of  thought 
proves  that  it  is  a  necessity  of  reality.  To  deny  this  means 
to  assume  that  the  mind  is  some  independent  spiritual 
nature  capable  of  engendering  an  order  of  existence.  Of 
course,  the  infant  undoubtedly  has  some  dim  sense  of  space, 
but  this  may  have  been  because  of  the  fact  that  the  universal 
reality  of  space  has  developed  in  the  human  mind  in  the 
course  of  its  evolution  a  spatial  sense,  because  it  helped  the 
mind  to  adjust  its  relations  to  the  external  order ;  and  so 
this  innate  spatial  sense  is  itself  evidence  for  the  reality  of 
space.  But  I  cannot  take  up  this  phase  of  the  question 
here. 

Thus  I  submit  this  Jewish  empirical  standpoint  to  the 
student  of  the  problem  of  space,  as  a  possible  solution. 


GLOSSARY   OF   SOME    HEBREW    PHILOSOPHI- 
CAL  TERMS   IN   CONNEXION   WITH   THE 
SUBJECT   OF   SPACE 

("OK  one  of  the  categories  denoting  place  '  where '.  nJNH  1END 
atwn  »j£b  iiDta  vby  pits'  kvw  iDipob  iDirra  (jun  "puna  sin 
(in  nn)  *vy3  in  n'33. 

TftJ.     See  mpD. 

7*713  magnitude.     bl22  inia  pure,  unoccupied  magnitude.     See 

Or  Adonai,  p.  4. 
fcpj  (Arab.  »-Jj».)  body.     nai3n  h»H)  *pa  MCT  DlpO  "jni5»  »0  ^31 

(n"3. 

D*13  (Arab,  ..^a.)  (1)  body.  Usually  applied  to  the  heavenly 
bodies,  (jworb'cb  a'sin  'ipn)  bWBOT  D^onan  wjd  iy3\ 
(2)  atom,  wi  iDvya  mp&n  33y*  wxena  (man  w$n)  man  mi 
(IV  /ion  d-d  yy"3&nr6  n»3nn  nany)  wwpba  mob  nan. 

DfcJ'Jl  (Arab.  «.«-*■).  Harizi  in  his  glossary,  prefixed  to  his  trans- 
lation of  the  Guide,  derives  it  from  Isa.  44.  14,  bl}*  DBW,  which 
he  interprets  •  And  the  bulk  he  increases '.  (1)  body.  See  Ruah 
Hen,  ch.  1,  D'pm  ')  "6  B*8»  131  ^3  Nin  Dtwn  Tttl.  Sometimes 
D£>ia.  See  Sefer  Mazref,  ed.  Gollancz,  p.  23.  It  is  noteworthy 
that  Harizi  invariably  renders  DDa"  by  epa.  DC?a  D33H  myaon 
Dtwa  impenetrability.     See  Or  Adonai,  p.  14.     (2)  atom,  JtT>3t5> 

owan   n^«  «na  dhd   D^aimp  o«ann  BWa  ii>  K*  nnsnn 
(a"a  ,t**D  .myii  ma»K)  (ttciiBR. 

jnflpn  continuity,  extendedness  "i^SN  "HW  mp3*in»  Ttxhb  WIT\V 
(?:py  \2H  ejDV  'ib  ieke)  um^v  bb^  n  VOW.  pannon  nea  (as 
distinguished  from  pianion  or  ppnnon)  spatial  magnitude.     See 

Milhamot,  p.  124,  p^nn*  k^b>  no  ^n  p^nno  p3inon  ncaw. 

jTT  atom.    (n*3  ,133.1  ^3£»k)  13^  pkn*  xta  Kin  m  pin  biaa  »3, 

117 


Il8  PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

nD*lin  penetrability.  i>3aiDtj>  pnn  rnipn  ^nan  nn»N  no  rbw 
(hd  paan  b^x)  ^iaa  Kip  xin  nn«  nan  nonane  innosn. 

Dlpnnn  continuity,  extendedness.  . . .  Dtwn  mw  JWI  niprrnnn^ 

(I,  2  /on  miD«)  Dtwn  mix  movy  pta  mpainn  mpbnonv  nn. 
nitD^finn  dimension,     Dn3ts>  no  nwpom  oiyn  jo  ii?  ww  asy 

(de>  /TDi  namx)  nviocsnn  'a  13  mavB>  njyaN. 
77)1  (Arab.  JJU)  pure  space.      D^iyn  n*V!P  DYip  131  rwi  t6& 

^l  b>yvb)  m|jd  nnt  *a  noNn$>  k^i  fpn  wn  >a  loxnij  ^n  ah 

(149  yfrw  'd^>  »3&ran. 
MlSSn  space-interval.     -\vx  Kim  (ppon  ro^an  pa  law  prmn 

(5  /n  YIN)  nbbn  N"lp\     Comp.  Aristotle's  Physics^  iv.  211  b  7 

Siacrnj/Aa  ti  to  fxeraiv  rav  etr^ctTcov. 

p7H  atom,  p^n  ik  na^nn  Nip*  Kin  D*a&j6  inrpi  pb^  ttbw  nam 
(n"D  /isan  i>3K>N).  See  &»£&,  I,  51,  ddj  niv"  jo  ni^np  po*  «h 
rrnsi  nana  n»^>  ?a!>K  ^>nd3n  ^y  jmai.  Also  ch.  73  nan 
npny*  jxa  nw  .  ,  .  ri^nNonoiw  nun^n  nin  jo  Naano  n^n 
Ti^S»3  i>Np  JND  n"«n  Dllp^BN.  Comp.  Fanari  in  Igi's  Almawakif, 
Cairo,  1907,  43,  i^LiU-o  £^».l  ^  u-Jy»  *-«*■.  Ibn  Tibbon, 
however,  has  for  \y>.  the  expression  pi>nn»  law  p^n.  Comp. 
Saadya,  Amanat,  36,  \yaSi  $  %js^.  Jjs  Jl  U-^  ^tJoJl  ^a/o.  J\j . 
This  last  expression  is  a  faithful  rendering  of  the  original  Greek 
terms  arofjiov  and  o-w/taTa  dStatpcTa.  Curiously  enough  Harizi 
renders  Pi  in  ch.  51  by  DHtyn,  well  deserving  Narboni's  remark 
nts>n  inrnN  nts>n  bv  inaas?  *d. 

PDTlPl  Karaitic  term  for  atom,  Wnan  iniN  D\smpB>  pin  inn 
(Y's  ,D«n  py)  naTin.    See  p^n. 

Wfi  occupied  space,  '  full ',  Gr.  irAeov.  pN  nan  tom  DB>  pN  DN 
(14 /n  -nx)  I^D  DB>.    Adj.  vbo. 

^¥D  one  of  the  nine  categories,  properly  designating  the  relative 
position  of  the  parts  of  the  body,  see  Rnah  Hen.  Often  identical 
with  nas  denoting  place  « where ',  hna  ia*KB>  DDNn  p  mtwi  Nini 
(n"s  ,D«n  py)  avon  nnpo  jo. 

Blpfi  (1)  space,  extensity.  n^N  pnn  NW  13*6  WDNn  Qlpenp 
(15  /n  Tin)  epp»n  nt^an  pa.  (2)  In  the  Aristotelian  sense,  as 
a  containing  body,    \twuon  ypnn  nnano  piycn  no^n  Nin  DipD 


GLOSSARY  119 

(01DWQ  nmzb  Dm:  "iSD)  DlDlpDn  nt3^.  Thus  it  corresponds 
to  both  toVos  and  x^Pa-  WD  DIpB  ^713  DIpD  corresponds  to 
the  Aristotelian  distinction  between  accidental  and  essential 
place;   see  Aristotle's  Physics,  iv.  211a.     WJ  nm  ^  *3  rW 

n^n  no  aw  pita  i?B>»n  nnv»  oipoi  bha  nipo  ni»ip»  w  b* 
n^an  wn  mJB>  «dd  nnv»  Dipoa  k*»j  d3»ki  &a  Dipo  sin 
26  /n^nd^d  ^>kw  '■£  mwp  nnjD)u  yawn  Doipnco  ^pm  nswn. 

(Berlin,  1898,  Ed.  Kaufmann.  (3)  Position,  direction,  Ger. 
Gegend.  Thus  Harizi  in  Moreh,  I,  4,  has  N^N  WE*  N^  D^yn  ''a 
VnpD  nvpl  D1p»2l  spJ,  for  which  the  original  reads  fftn  K^>  ix 
nvKij?N  pyai  rini  "'Si  ndd:  &6n  pys^.  The  meaning  of  this 
passage  is  not  made  clear  by  Scheyer  (see  his  note  a.  /.),  nor  by 
Munk,  who  renders  rini  ^21  by  '  d'un  certain  cote  ' :  Maimonides 
here  refers  to  the  Mutazilite  theory  that  sight  can  only  be 
caused  by  an  object  occupying  a  certain  position  (I^*.)  relative  to 
the  seer,  but  as  the  Deity  is  beyond  space  relation  to  any  object, 
it  can  never  have  a  visual  sensation,  a  theory  much  disputed 
by  the  Asherites.  See  M.  J.  Mailer's  translation  of  Ibn 
RushcPs  Philosophic  u.  Theologie,  pp.  70,  71.  (4)  D1p»  TID11 
occupies  space  conveying  the  sense  of  impenetrability,  Cpmn 

D^pmnt?  aa-mo  p*w  run  ....  mpo  rmt*  vb  i»in  ^jn  wi  ab  on 
dpjq  ovi  man  yj»:  win  *wn  nro  -\m  Dipon  nnta>  iDin  ^ya 
(T>  /n  Tin).    The  meaning  therefore  of  the  very  difficult  passage 

in  Moreh,  I,  51,  ^laan  v**  bza  nipca  u»k  man   tajm 

(others  read  Tin»n  nnD"1),  is  that  though  an  atom  is  in  itself 
unextended,  it  still  controls  certain  space-limits  within  which 
no  other  atom  can  penetrate.  Munk's  interpretation  of  the 
passage  (see  a.  I.)  hardly  seems  to  me  justifiable.  He  reads 
into  it  a  certain  Leibnizian  theory  that  the  atom,  like  the  mathe- 
matical point,  occupies  an  atom  of  space  only,  an  interpretation 
little  substantiated  by  his  own  citation  from  Gorgani's  Kitab 
al-Tdrifat,  which  is  as  follows  :  pJ^-aJl  yt  c^w^Ji5c:ll  jjlc  ijS^W 

ij^+X&W  JJL_C  j!lJJ  olaol  s-*i  li-^j  *~^U  JuLiJ  t^jJI  *A^dl 
jLs-»-o  j-s-z  J    (%--^^  Xi*-o   ^   &  Ik  <L  i   t^JJl   -*yz\\    cl^iJI  jJi 

^,-aJI  j.sb^S,  i.e.  the  term  '  makanun'  is  ascribed  only  to  such 


120         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

an  object  which  occupies  a  certain  space  and  also  permeates 
it  with  its  own  dimensions,  while  'hayyazun'  is  ascribed  to 
objects,  both  extended  and  unextended,  which  only  occupy 
it  but  do  not  completely  fill  it  with  their  voluminousness.  If 
nowjl»  were  an  atom  of  space,  it  could  not  be  ascribed  to  a 
jLu-»  {Ji'.  Our  interpretation  is  furthermore  corroborated  by 
Hadassi's  definition  of  the  term  ^133,  viz.  inn»K3  ^3i1»n  pnn 
(.Y'd  ,D"n  yv)  yyyz  baaion  boa  Kip*  Kin  nn«  nan  nonano. 
So  Ibn  Rushd,  in  commenting  on  the  term  £4^,  writes  in  the 
first  part  of  his  Masail:  £  »j|  L^*.  ^y  ^\5   UJ^a  x>jj>  esDlJ^ 

....  »,L«j  y  »»i-j^j.  Lastly,  Ibn  Ezra,  who  takes  the  stand- 
point of  the  Mutakallimun,  remarks  mpD  33JP  lKXOna  Dian  im 
vnump  spa  DBDsnn  onDnam  ....  iDipoa  ko»  nan  yao^i  i»*ya 
nainy)  '01  ,p»iyi  anm  *piK  o  tw  span  mi  yonyna  n»Dann 
(noann,  where  the  meaning  is  clear;  i.e.  every  spatial  body  is 
composed  of  atoms,  each  one  unspatial  by  itself  yet  controlling 
certain  space-limits  within  which  no  other  atom  can  penetrate, 
so  that  the  extensity  of  a  body  is  due  to  the  empty  spaces 
between  the  spaceless  atoms.  Other  Hebrew  expressions  used 
for  the  Arabic  j-^-JJ  Jjl^j  are  DlpD  k!>D*  (see  JDP  D^iy,  p.  15) 
Dipo  aay*  (see  ncsnn  nany)  mpe  pop  (q.  v.)  oip»  tnan^  (see 
quotation  from  nicya  "1BD  in  Schreiner's  Kalam,  p.  37). 

pPHB  (1)  distance,  (fa  /n  nis)  n^an  *nbab  pmon  nvpnn  nvwaK. 
(2)  dimension,  naba  'an  Ypmn  nvo  Kin  iDaan  n^as  Dt?a  ya»ne> 
(DB>),  identical  with  pnn,  q.  v. 

&|DinD  augmentable.     ejDino  ^K  epine  infinitely  augmentable. 

(334  ,'n  nicnbr:)  spirit  no  ^k  naD»n  nr  spwp  n»n  qki. 

pSflfitt  divisible.  pbrfflD  ^K  pbnn»  infinitely  divisible,  lain  nn 
no  ^k  pbnn*  Kins?  nyb  nan  pr  Kinp  nca  pn  Ki»»B>  a*m> 
(334  /n  nicnb»)  pbnnn?.  pbnn*  k^b>  n»  ^k  pbnn»  finitely 
divisible. 

DDIpftfi  a  thing  in  space,  contained.  taoipne  ^30  DlpO  f'KP 
(15  ;pp  o!>iy). 


iTflpJ  (i)  point.  See  definition  in  mnPnm  nrVBWl  tCW  by 
Abraham  bar  Hiyya,  Berlin,  1912,  where  a  number  of  geo- 
metrical terms  are  defined.    (2)  niJDp  DlTipJ  atoms,     pp  Nine 

0"q  Xd  iHWOK)  V^tt  k!>  ib>n  D^nn  om  nuop  nmpi  dto. 
DDIS  occupies  space,     "inbir  y:io  oipoa  poiy  Kinti>  pnn  artno) 
(a'a  ,D*n  py)  >^  D1P03  tfw». 

D'pbS  pIDS?  the  act  of  occupying  space.  ipiDy  VN\  pin  nWKl 
(DC)    D1P02.      Sometimes  p1Dy    alone.      way  qpWB  DtJ>  DlpO 

(xx,  at?)  ipn  piDyb  pwrw. 

DXtf  (prop,  substance)  (1)  atom.     V3M  nyi  $>y  33189  DP3  fcj  *3 

(y"3N-6  nirrc  isD)  wai  D'csyo  nynn  hpe>.    (2)  ma  oxy 

(Arab.  &ji}\j*M,  not  to  be  confused  with  ^i-dl^a^ll.  See 
Ibn  Rushd's  Kitab  al-Masail,  part  I)  atom,  corresponding  to 
Joannes  Philoponus's  ftepi^a  ova-ia  (cf.  Schreiner's  Kalam,  pp.  9, 
45>  note  2,  and  Munk,  Guide,  I,  186)    immw  *VW1  DXynt? 

(a"y  X'n  /'id)  one  oi>o»  «h  Dnn  onpM. 

MXS  (prop,  side,  limit,  Arab,  i^)  Karaitic  term  for  relative 
space.  See  Ez  Hayyim,  ch.  4,  bom  DBKn  |D  pin  DNX  njn 
(comp.  Falaquera's  Moreh  ha-Moreh,  Presburg,   1837,  p.  62, 

n*33n3  haon  3"n  . . .  hson  n,  m  mm  nwn  yn).  r6nm  dip»3 
niny  '3  thtrv  wn  pww  yjnano  n^i  pw  n^  i&wv  xi>  wmn 
yyurasw  yyian»m  niny  w  nine  wk  emnn  r6nm  nnx  dipds 
HNsa  ?awn  kwi  rmnn  u»?  rrari  dko  immpi  w*reo  "in«  BHnrv 

HNS  l"6tt.  It  is  probably  in  this  sense  that  Hadasi  uses  the 
term  in  Eshkol  Hakofer,  ch.  29,  b»3V  7X0  Kin  pyi?  n&oan  <3 
nKD3  IK  D1pB3.  See  also  ch.  28.  Comp.  Sefer  Ne'imot,  quoted 
in  Schreiner's  Kalam,  p.  37,  Pisnni  pDyni  NXIDD  ON  "WK  naTinni 

wan*  ah  pDy^  n^  nv»*  dk  icn  Nin  yaxm  tpyfiKn  ?3pm  nttfi 

D1p».     Ibn  Ezra  also  uses  the  term  in  his  noann  nany. 
*N32D  empty  space,  void  (Gk.  Kev6v).     myJDVU  BnDIKn  D.m3D  *fi^ 

(15  /n  -iik)  we  rrona  dp  e*  n"33  oca.    As  an  adj.  n»; 

see  zifo/.,  14  b. 
tp  an  imaginary  line  composed  of  mathematical  points  or  of  atoms. 
See  Ez  Hayyim,  ch.  4,  and  Ibn  Rushd's  Masail,  part  I. 


122         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 

D"J!"Tn  (Arab.  uyloUj^)  atoms,  tsmio  on  ncx  D^nnn  Dm 
(:"a  X°  Twrntu)  pbnnv  pup  p^nai  pn  bo  piai  paaa  Dnatrnoa. 

pm  (i)  interval,  stereometric  content,  the  Aristotelian  Siao-r^/m. 
(15  b  /n  tin)  e|»pcn  nvbn  pa  -k?k  pmn  wii  na-6  vidnh  DipDnc; 
(2)  dimension.  D^iai  Cpm  =  dimensions  of  pure.  rttffl 
(dk>)  dcj  *pm  ^apb  *tiKi  mpon  oayy  D^naan  D^pmn. 

rilpl  void.  a"a  d^s»k»  onanon  noan  ip*jj  \w  ttnaien  wip 
(!>  73  ,3*10)  NVDJ  nip^ntr.    Harizi  uses  the  word  Dpn  for  a  noun. 

ntDfc?  plane,  surface  composed  of  four  atoms.     Cp.  1p. 

TVfo&  dimension,     npforn  ann  *int«m  "piK  a^  DTn^n  nriNi 

pDiy.      See  Moritz  Lowy,  Z>ra"  Abhandlungen,  Berlin,   1879, 
Heb.  sect,  p.  n. 
Jr?3n  (1)  limit,  end  =  ?]iD;  rv^an  i»j?3,  finite;  jvl>an  by*  *r6a, 

infinite.      (2)  Limiting  surface,  superficies.      Cp.  the   current 
Aristotelian  definition  of  Makom,  ^naa  nit?  ^pD  rvbn. 


INDEX 


Aaron  of  Nicomedia,  44,  45,  50,  55, 
56,  66. 

Abrabanel,  Don  Isaac,  I,  37,  39,  43- 
5,  66,  67,  70.  85-7,  106,  113,  116. 

Abraham  bar  Hiyya,  40,  44,  65. 

Absolute  Space,  61-7  ;  Aristotelian 
notion  of,  63  ;  the  traditional  view 
in  Jewish  philosophy,  63  et  seq. ; 
Gabirol,  Abraham  bar  Hiyya, 
Joseph  ibn  Zaddik,  Abraham  ibn 
Daud,  Aaron  the  Karaite  and 
Gersonides  on,  65,  66 ;  Crescas 
challenges  the  Aristotelian  con- 
ception of,  66-9 ;  his  influence  on 
Albo,  68  et  seq. ;  Abrabanel  accepts 
the  Aristotelian  definition  of,  71  ; 
summary  of,  118. 

Abu  Hamd,  43. 

Achilles,  in,  112,  115. 

Acht  Biicher  Physik,  15. 

Albo,  Joseph,  55,  66,  68,  70. 

Aquinas,  Thomas,  86. 

Archivfiir  Geschichte  der  Philosophic, 
30. 

Aristotle,  4,  5,  7,  8,  14-21,  23,  27, 
33.  36,  37,  39,  45-5°,  55,  57,  62- 
4,  66-72,  77,  85,  88,  91,  93,  94, 
98,  99,  103,  104,  112,  113. 

Aspects  of  Rabbinic  Theology,  28. 

Atomism,  see  Infinite  Divisibility. 

Attributenlehre,  64. 

Averroes,  43,  85. 

Baeumker,  33. 

Bahya,  93,  94,  105. 

Bergson,  Henri,  2. 

Bibago,  Abraham,  44. 

Bible,  27,  62. 

Book  of  Cones,  98,  108. 

Book  of  Creation,  see  Sefer  Yezirah. 

Botarel,  Moses,  67. 

Brothers  of  Purity,  36. 

Cohen,  Hermann,  2. 
Conception  of  the  Infinite,  ior. 
Cosari,  27,  28,  49,  52,  78,  92. 
Crescas,  41,  63,  66  72,  78-86,  103-5. 
Delitzsch,  Franz,  44. 


Democritus,  47,  49. 

Descartes,  20,  25,  28,  34,  35. 

Dieterici,  36. 

Die  Religionsphilosophie  des  Saadia, 

92. 
Dogmas,  see  Ikkarim. 
Drei  Abhandlungen  by  Moritz  L6wy, 


Elijah,  del  Medigo,  37. 

Empirical  Space,  22-46 ;  Plato  on, 
5-14,  33-4  J  Aristotle  on,  33-4 ; 
Descartes,  34  ;  Kant,  34-5  ;  Aris- 
totelian conception  shared  by 
Saadya,  Maimonides,  Samuel  ibn 
Tibbon,  36;  Elijah  del  Medigo, 
Abrabanel,  Jehiel  of  Pisa,  37; 
pseudo-Platonic  conception  repre- 
sented by  Isaac  Israeli,  the  elder, 
32  ;  Gabirol,  38  et  seq. ;  Abraham 
bar  Hiyya,  40 ;  Joseph  ibn  Zad- 
dik, 40 ;  Abraham  ibn  Daud  on, 
41  ;  the  latter  followed  by  Joseph 
ibn  Aknin,  43 ;  Moses  Narboni, 
Shem  Tob  ben  Shem  Tob  and 
others  share  the  pseudo- Platonic 
view  on,  44  et  seq.  ;  Abrabanel  on, 
45  ;  summary  of,  1 10. 

Emunah  Ramah,  42,  66,  95. 

Emunot  we-Deot,  22,  24,  36,  50,  52, 
62,  91. 

Epistolae  ad  P.  des  Bosses,  55. 

Eshkol  Hakofer,  45,  49. 

Es  Hayyim,  44,  50,  55,  56,  66,  96. 

Ethics,  93,  101,  107. 

Euclidean,  69. 

Festschrift,  Steinschneider's,  27. 
Fons  Vitae,   26,  38,  39,  53,  54,  65, 

96 ;  see  Mekor  hayyim. 
Fullerton,  101. 

Gabirol,  26,  27,  31,  36,  38-90,  93,  96, 

98  et  seq. 
Galen,  27. 

Gersonides,  57-60, 65, 66,75-8,80,86, 
91,  97-9,  101,  102,  104,  106,  109. 
Geschichte  der  alien  Philosophic,  7. 


I23 


124         PROBLEM    OF    SPACE    IN    JEWISH    PHILOSOPHY 


Greek    Philosophy    to     the    time    of 

Socrates,  7. 
Grundriss  einer  systematischen  Theo- 

logie  des  Judentums,  24. 
Guide  for  the  Perplexed,  55,  56,  6r, 

72,  96,  98. 
Guttmann,  39,  93. 

Hadassi,  Judah,  45. 

Hakarmel,  27. 

Hebrdische    Uebersetzungen,   67,    98, 

105. 
Heraclitus,  12. 
Hirschfeld,  27. 

Histoire  des  langues  semitiques,  1. 
Hobot  ha  Lebabot,  40. 
Horowitz,  Saul,  22,  26,  28. 
Husik,  Isaac,  39. 

Ibn  Aknin,  Joseph.  27,  42,  44,  45. 
Ibn  Daud,  Abraham,  42,  44,  45,  65, 

73,  75- 

Ibn  Ezra,  Abraham,  72. 

Ibn  Latif,  Isaac,  73,  78,  97. 

Ibn  Rushd,  119,  121. 

Ibn  Zaddik,  Joseph,  28-31,  41,  44, 
65,  67,  72,  78. 

Iggerot  ha-Rambam,  22. 

Ikkarim,  56,  66,  68,  73. 

Infinite  Divisibility,  46-60  ;  Aristote- 
lian doctrine  versus  Atomism  of 
the  Mutakallimun,  47-9;  Judah 
Hadassi  as  well  as  other  Jewish 
thinkers,  with  the  exception  of 
ibn  Ezra,  uphold  the  Aristotelian 
theory  of,  49 ;  Isaac  Israeli  the 
elder  on,  49  et  seq. ;  Saadya  in- 
troduces Zeno's  paradoxes,  59  ; 
Gabirol's  arguments  in  favour  of, 
53  ;  Maimonides  on,  55  ;  Gerso- 
nides's  solution  of  Zeno's  puzzles, 
57  et  seq.  ;  summary  of,  111-18. 

Infinite  Space,  88-109 1  Aristotle's 
theory  of,  88  ;  potential  versus 
progressive  infinity,  the  former  at 
first  prevalent  in  Jewish  thought, 
91  ;  Saadya  on,  92  ;  Bahya  and 
Gabirol  on,  93  ;  ibn  Daud's  proofs 
against,  94-5 ;  Maimonides  and 
Narboni  disprove  the  contention 
of  the  Mutakallimun  against,  96-8  ; 
Isaac  ibn  Latif  and  Isaac  Israeli 
on,  98  ;  Gersonides's  contribution 
to  the  problem  of,  98-103 ;  Cres- 
cas's  criticism  of  the  Aristotelian 
theory  of,  104-9;  summary  of, 
1 13-15. 


Isaac  Israeli  the  Elder,  i,  22,  38,  45, 

49,  53- 
Isaac  Israeli  the  Younger,  50,  56, 98, 

99. 

Jehiel  b.  Samuel  of  Pisa,  37. 

Jowett,  6. 

Judah  ha-Levi,  28,  91. 

Kalam,  37,  49,  56,  71,  96. 

Kant,  8,    14,   20,  34-6,  46,  57,  86, 

114,  115. 
Kaufmann,  D.,  64. 
Kohler,  K.,  24. 

Leibniz,  55,  112. 

Leisegang,  2. 

Levi  b.  Gerhon,  56. 

Light  of  God,  see  Or  Adonai. 

Locke,  John,  8. 

Lflwy,  Moritz,  42. 

Maimon,  Salomon,  74. 
Maimonides,  36,  40,  55,  56,  62,  73, 

95,  96>  98,  99,  105,  109. 
Mekor  Hayyim,  27,  39,  65. 
Maker," H.,  22. 
Melanges,  26. 
Metaphysics,  7,  88, 
Microcosm,  2,  8,  29,  31,  40,  41,  65, 

72,  73- 
Mtf'alot  Elohim,  71,  85,  89,  106. 
Milhamot  Adonai,  56,  66,  75,  96,  97, 


Minhat  Kenaot,  37, 69. 
Monads,  55. 

Moreh,  see  Guide  for  the  Perplexed. 
Munk,  1,  26,  27,  49,  55. 
Mutakallimun,     47-9,     55,    56,    62, 
84,  91,  96. 

Najimites,  51. 

Narboni,  44,  67,  72,  73,  95,  98,  109. 

Naturanschauung,  36. 

Neumark,  David,  39. 

Newton,  Isaac,  28,  73. 

Olam  Katan,  see  Microcosm. 
Opinions,  see  Emunot  we-Deot. 
Or  Adonai,  41,  67,  69,   75,  85,  89, 
98,  104,  105,  107. 

Palquera,  39. 

Philo,  2. 

Philosophic  des  Salomon  ibn  Gabirol, 

by  Guttmann,  39. 
Physics,  by  Aristotle,  5,  33,  55,  64, 

65,  7°,  88. 


Plaio  and  the  Older  Academy,  4,  5, 

11,  21,27,  33.  64,69,  70. 
Platonische  Studien,  5. 
Prantl,  15. 

Principes  by  Descartes,  34. 
Problem   der  Materie  in  der  griechi- 

schen  Philosophie,  33. 
Pseudo-Platonism,  33,  35,  38,  45,  46 

et  seq. 
Psychologie  beidenjudischen  Religions- 

philosophen,  22,  26. 
Psychologisches  System  des  Maimo- 

nides,  36,  40. 
Ptolemy,  63,  96. 
Pythagoreans,  7. 

Rab  Pealim,  73,  98. 

Raumtheorie  im  spateren  Platonismus, 

2. 
Religionsphilosophie  des  Saadia,  92. 
Renan,  1. 
Ritter,  7. 
Ruah  -Hen,  37. 

Saadya,    1,   28,  29,  49,  50,  53,  57, 

62-4,  91. 
Samuel  ibn  Tibbon,  36  et  seq. 
Saul,  a  pupil  of  del  Medigo,  45. 
Scharistani,  51. 
Schechter,  S.,  28. 
Scheyer,  36,  37,  40. 
Schmiedl,  37,  39. 
Schreiner,  49. 
Sefer  ha-Gedarim,  68. 
Sefer  Musar,  27. 
Sefer  Yesodat,  38,  49,  53. 
Sefer  Yezirah,  29,  64. 
Sheelot  Shaul  ha-Cohen,  37,  39. 
Shem  Tob  b.  Shem  Tob,  44,  105. 


:x  125 

Simplicius,  69,  70. 
Spinoza,  2,  93,  97,  101,  107. 
Steinschneider,  2,  21,  67,  98,  105. 
Studien  iiber  Religionsphilosophie,  37. 

Tabrizi,  105,  107. 
Thomas  Aquinas,  86. 
Timaeus,  5-9,  11. 
Tractatus  de  Anima,  27. 
Tree  of  Life,  see  Es  Jfayyim. 

Void,  71-81  ;  Aristotle  on,  17  ; 
Aristotelianism  versus  Kalam,  71 ; 
Jewish  philosophy  at  first  denies 
existence  of,  72;  Joseph  ibn 
Zaddik  follows  Aristotle,  72 ; 
Maimonides  and  Ibn  Latif  on,  73  ; 
relative  versus  absolute  void,  74  ; 
Gersonides's  argument  against, 
and  his  difficulty  with  the  word 
•  beyond ',  75  et  seq.  ;  Halevi  on, 
78 ;  Crescas's  reply  to  Gersonides 
and  his  refutation  of  the  four 
Aristotelian  arguments,  78-84 ; 
Abrabanel's  reaction,  85 ;  his 
evolutionary  theory  of  the  psychic 
finiteness,  86  ;  summary  of,  11a- 
"3- 

Wars  of  God,  see  Milhamot  Adonat. 
Works  of  God,  see  Mif'alot  Elohim. 

Yesod  Olam,  50,  56,  99. 

Zeller,  5-7,  11. 

Zeno  of  Elea,  1,  4,  51-3,  57,  59,  64, 

65,  84,  115. 
Zifrinowitsch,  28. 


VITA 

ISRAEL  Isaac  EFROS,  born  at  Ostrog  in  the  province 
of  Volhynia,  Russia,  in  1890,  obtained  his  elementary- 
education  from  his  father.  At  the  age  of  thirteen,  he 
entered  the  Yeshibah  of  Mir,  where  he  attended  the 
discourses  of  R.  Elijah  Baruch.  The  following  year  he 
came  to  America,  where  he  pursued  his  Talmudical  studies, 
and  was  ordained  Rabbi  in  his  eighteenth  year.  He  then 
entered  New  York  University,  where  in  19 13  he  received 
the  degree  of  B.A.  He  then  took  courses  at  Columbia 
University,  where,  specializing  in  Semitic  languages  and 
in  philosophy,  he  obtained  the  M.A.  degree  in  I9i4and  the 
Ph.D.  degree  in  1915.  In  that  year  he  was  also  graduated 
from  the  Jewish  Theological  Seminary  of  New  York.  He 
has  occupied  a  Rabbinical  position  in  Lynn,  Mass.,  later  in 
Hoboken,NJ.,  and  is  now  principal  of  the  Hebrew  Institute 
of  Baltimore,  Md.  He  has  contributed  to  Hebrew  and 
English  periodicals. 


IOAN  DEPT. 

.         _  .u„  i«t  date  stamped 


.SSfifiBSBt 


ripneral  Library     . 


383545 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


